lost in the fog, and he tricks Jim into thinking he’s going to shore to see where they are on the river but really intends on turning Jim in as a runaway slave.

Both boys also like to tell “whoppers,” as Twain would call them. They tell elaborate stories about pirates and highwaymen.

Tom and Huck are two boys who are typical for their age.  They want to experience adventure and have fun.  

I'm afraid you will have to include the quote that you would like us to analyze if you would like one of us to intelligently answer this question.

I am guessing it is the following (arguably) most famous quote that Huck spoke in chapter 15:

Huck’s racism prevents him from seeing that Jim argues well.

It was fifteen minutes before I could work myself up to go and humble myself to a nigger; but I done it, and I warn't ever sorry for it afterwards, neither. I didn't do him no more mean tricks, and I wouldn't done that one if I'd a knowed it would make him feel that way. (15.49)

What this quote says to me is that although Huck was raised to be racist (note the use of the N word), that he has the character to break out of his upbringing and see people for who they are. He still sees Jim as lower than himself as evidenced by the fact that it took him so long to get up the courage to "lower" himself to a black man in an apology.

 However, the fact that he felt good about the apology afterward...and that he vowed never to make even a black man feel badly because of him in the future...shows that Huck is a thoughtful, independent, moral young man who isn't afraid to buck society if he thinks it is wrong.

Huck Finn has a lot of really interesting character traits that make him a very unique kid.  He is clever; he anticipates his father showing up and wanting to steal all of his money, so to avert this situation, he goes to Judge Thatcher and tells him of the money, "I want you to take it," so that when his Pap shows up demanding his money, Huck won't have any to give to him.  The Judge, having "bought" it off of Huck, will own, it, leaving Pap no legal rights to the money.  Huck also demonstrates his cleverness in his awesome escape from the cabin in the woods.  He stages the entire event to make it look like burglars robbed the place, killed Huck and dragged his body to the river, and then took off the opposite direction.

Huck is also ponderous, meaning, he thinks about things a lot before acting on them.  He ponders the meaning of prayer before deciding,

"I couldn't see no advantage about it--except for the other people; so at last I reckoned I wouldn't worry about it any more, but just let it go." 

He ponders slavery quite a bit throughout the book, and always decides to help Jim over his conscience bugging him about the implications of helping a runaway slave.  Any odd thing he hears, or thing that he is curious about, he tests it out, mulls it over, and comes to his own conclusions.

Huck is also curious, adventurous, loyal, and funny.  I hope that those thoughts help; good luck!

Tom and Huck are both young, naive, and adventurous.  Both of them are interesting in doing exciting things, but Huck is more interested in doing things for the right reason.

Twain wrote Huck Finn as a foil, or contrast, to Tom Sawyer.  Tom is a simple-minded kid who is only interested in adventures.  His conscience is wholly dictated by the social order.  Huck, on the other hand, actually thinks for himself.  He is the real rebel.  While Tom follows fun, Huck follows his conscience.

Huck struggles to develop his conscience throughout the book.  A good example of this is his reaction to the idea that people who side with slaves go to Hell.  Huck has to decide “forever betwixt, two things,” meaning following his conscience or following society’s norms.  He writes a note telling Miss Watson where her runaway slave Jim is, but he cannot send it because Jim has become his friend.

“All right, then, I'll go to hell”—and tore it up. (ch 31, enotes etext p. 141)

By contrast, Tom never questions society’s norms, laws and rules.  It never occurs to him to free a slave.  He only helps Huck free Jim because he knows Jim is already free, so there is nothing immoral or illegal about it.  He concocts a ridiculously complicated and risky scheme, never telling anyone they are freeing a freed slave.  Huck thinks he’s doing the right thing, but he is shocked that Tom would.  After all, he doesn’t expect Tom to go to Hell.

This changes Huck’s opinion of Tom.  Huck thought Tom was intelligent and a good friend.  After the incident with Jim, Huck realizes that Tom does not really have a conscience, because he is willing to free the slave.  This is illegal and, according to Huck, wrong.

THE FIRST TIME I catched Tom private I asked him what was his idea, time of the evasion?—what it washe'd planned to do if the evasion worked all right and he managed to set a nigger free that was already free before (ch 42, p. 191)

At the end, Huck decides he’s too old for childish games, and he goes off on his own—without Tom Sawyer.

Huck is much more logical and practical than Tom is.  Tom has grand visions and imaginative dreams fueled by the fact that he has read one too many adventure novels in his day.  As a result, he complicates every single issue in order to make it more adventurous and exciting.  He forms a "band of robbers" and puts these young boys through a whole list of ridiculous shenanigans, all in the name of meeting up to his high expectations of what a grand adventure should be.  He submits Jim to days of imprisonment at the end of the novel just so that he can rig a more "realistic" (which is, in reality, not more realistic) prison and escape scene.  For Tom, all else is sacrificed on the altar of a fantastic adventure.

Huck is much more realistic, and is often dragged along by the sheer force of Tom's enthusiasm for an adventure.  Huck is a smart kid who wants to go about doing things in the most efficient and logical way possible.  He sees solutions to problems, and goes about fixing them.  He is also more of a tag-along than Tom is.  Tom rustles up people and situations, taking charge and causing commotion.  Huck pretty much goes with the flow, doesn't like ruffling feathers, and is much more about keeping the peace.  As he mentions on the raft with the duke and the king,

"I learnt that the best way to get along with his kind of people is to let them have their own way."

Huck doesn't challenge the status quo; he reads people well and does what it takes to keep things smooth and happy.  For Tom, that is boring--where's the excitement in that?  Tom often chastise Huck for being no fun, and having no imagination or sense of thrill.  It just shows the differences between these two timeless characters.  I hope that helped; good luck!

Huck is an intelligent, thoughtful, and resourceful boy who is about thirteen as the novel opens. Because of his life circumstances, he has had to live by wits, which has made him practical, quick-thinking, and observant.

What has most formed Huck is his outsider status. As a person who has lived his life largely on the fringes of respectable white society in St. Petersburg, Missouri, he is an amalgam of any number of superstitious ideas, real facts, practical know-how, and a shrewd, if usually innocent, ability to assess a situation. Both the comedy and the pathos in the novel arise from his tendency to think and process situations in his own way.

Because of his outsider status, Huck is able to assess people based on how they behave rather than on their social status. He has imbibed his society's racism, for example, but not enough to prevent him from traveling with Jim, seeing the genuine human worth in him, and learning to love this friend and father figure. Likewise, without the intellectual background to assess the ridiculous claims of the Duke and King, he is able to quickly discern their dangerous, sociopathic natures and take precautions.

Huck is likewise quick to discern the cultural and religious hypocrisy of the feuding Grangerfords and Shepherdsons. His lack of pretension, goodhearted nature, and frank appraisals of reality make him an endearing and enduring character.

Tom Sawyer is well-read in comparison to Huck Finn, but lacks Huck's capability of dispassionate consideration. Where Tom energetically tackles problems using his imagination, Huck finds that practical reflection can sometimes help to temper the imagination.

This difference is not as slight as might be believed at first notice. Tom's insistence on "adventure" leads rather directly to a bullet in his leg. This insistence also sends the Phelps household into a frenzy while forcing Jim to sleep with snakes, rats, and spiders. 

Tom does not demonstrate a knowledge of some of the humbling lessons that Huck has learned over the course of his journey down river. While Huck brought himself to apologize for insensitive behavior toward Jim, Tom inflicts punishment after punishment on Jim simply for his own amusement. He expresses no remorse when he finally breaks the news that Jim has been free since he (Tom) arrived and the "adventures" were all for fun. 

In all the dealings that Huck has with Tom, we see another significant difference between them in Tom's leadership ability. Tom is a leader and Huck is not.

Neither Huck nor Jim approve of Tom's "adventures," although they feel compelled to submit to his authority in such matters.

No matter how outlandish Tom's ideas are, he is capable of demanding agreement and even fealty. 

Huck, more humble and uncertain, is portrayed as deferential, even to those who would abuse him. 

...despite his “street smarts,” Huck is vulnerable to the characters he meets on his journey down the river...

Huck knows that Tom, like the King and Duke, is not right in all he says, yet he goes along with the plan making little noise about it.

Tom is an imaginative, rather impractical adventurer.  He is well-read, and as a result often gets the two of them in a lot of trouble and mischief when it wasn't necessary.  Take for example, the "rescue" of Jim.  They could have gotten him out of the shed immediately, but because of Tom's insistence on making it like it is in the books that he has read, Jim has to stay for much longer, suffer quite a bit, and it ends up in Tom's injury.  So, Tom is a much more adventurous type, in the sense that he likes to come up with games and schemes to entertain himself.

Huck on the other hand lives in a much more logical and practical manner.  His entire life is an adventure--he doesn't need to make up schemes to stay busy and active.  His father makes his life one big mysterious adventure.  Huck is less "civilized" in the sense that he doesn't like school or reading, isn't educated like Tom, and so likes to be more free and unrestrained by society's customs.  Tom comes from a more stable setting and is educated, so has to invent action for himself.  Huck has a very practical head on his shoulders, and really thinks through the implications of his decisions.  He plans smart rescues (like when he escaped his father), and reads people pretty well.

I hope that those thoughts helped; good luck!

Tom is imperious and has little regard for the feelings of others. We see this in Tom's rather rigid treatment of his friend Huck and also in his indifference to the suffering of his aunt during the period of Jim's planned escape. 

Huck does consider the feelings of others and agonizes over them. He is not purely empathetic or sympathetic. He acts selfishly and cruelly from time to time, but he demonstrates these positive qualities on several significant occasions. 

Warnging the Wilks family about the King and the Duke is one place where Huck shows his ability to understand the feelings of others. Also, his choice to help Jim escape from the Phelps farm serves as an example of Huck's empathy. 

Huck does defer to others to a considerable degree as well. This is something Tom never does. In Huck's willingness to be led, he acts in ways that he regrets, hurting people's feelings or doing wrong because the King, the Duke, or Tom has told him to do so.

In The Adventures of Huckleberry Finn, Huck and Tom, while both mischievous and both full of a desire for adventure, are different in that Huck has a more mature sense of the world, while Tom remains stuck in childhood. These differences stem from their upbringings and are made evident in the later chapters of the novel when Huck is fighting for Jim's freedom, while Tom, who knows Jim has been set free, continues to want to play an adventure game.

Huck grew up poor and physically abused by his father. In Huckleberry Finn, his father kidnaps him and takes him to an island. Huck, instead of thinking this an adventure, fears for his life and comes up with an ingenious plan to fake his own death.

His entire "adventure" in this novel is about him escaping danger and protecting Jim. Huck, unlike Tom, has nothing to return to—no safety net, so to speak. He has no Aunt Polly. He's even condemned himself to hell for helping a runaway slave. He just has his life and Jim's to worry about.

Tom, meanwhile, has a safety net. His adventures end when he wants them to end. He grew up in a nice home with food on his table every night and without fear of physical harm.

These differences in primary characteristics become evident when Aunt Sally keeps Jim prisoner. Huck has shown he'd risk everything to set Jim free, but ends up relying on Tom, who has always been the leader of their adventures. Tom, meanwhile, already knows Jim is free, that Miss Watson set him free when she died, but insists on playing some type of adventure game, including covering him with snakes, spiders, and other critters to make his escape more believable.

It is not an accident that at the end of the novel, while Tom returns to St. Petersburg hoping to have more "adventures" and probably to live out most of his life, Huck decides to start new by moving west.