Lord Henry and Basil essentially represent both sides of Dorian Gray. They are foils and mirrors of one another; that is, they are similar, but in other ways they are different forces that pull Dorian in different directions. Most importantly, they are both pivotal agents that move the plot forward.

Basil, a humble painter and friend of the "fashionable set," describes himself much as any artist of the time might:

You know we poor artists have to show ourselves in society from time to time, just to remind the public that we are not savages.

This snippet is significant because it shows us that Basil is a product of his class system, one which completely separates people based on their social standing, money, possessions, and family name.

As such, Basil is aware that he belongs to a lower "rank" in society, and, by default, he is prone to hold his "betters"—that is, those with money and titles—at a higher esteem than he should.

We see that he has no problem understanding that there is a pecking order in society when he accepts Dorian's constant snubbing of him once Dorian meets Lord Henry. It is almost as if he expects Dorian to be mean and cold to him, only because Dorian has the best of everything going for him: looks, youth, beauty, class, fortune, and the support of high society.

Hence, those are Basil's key traits that separate him from Lord Henry: his understanding of being of a lower rank, his willingness to give in to the higher ranking, and the fact that his love for Dorian carries a heavy pathos, which is not surprising coming from an artist with a dramatic sensibility and a tendency for nostalgia.

Basil shows that he also has a deeply held sense of morality when he tells Dorian, upon seeing the real picture of Dorian Gray in chapter 13,

Pray, Dorian, pray. . . . "Lead us not into temptation. Forgive us our sins. Wash away our iniquities." Let us say that together. The prayer of your pride has been answered. The prayer of your repentance will be answered also. I worshiped you too much. I am punished for it. You worshiped yourself too much. We are both punished.

We could argue that Basil represents the part of Dorian Gray that can still be redeemed. Many times Basil suggests to Dorian to watch himself, to not be mean to Sybil Vane, to take good guidance. Basil is by no means perfect, but he is indeed redeemable.

Lord Henry is the opposite. He is rich (or lives above his means, anyway) and titled, and as such he is also hedonistic, feels entitled to everything, and is full of himself. He has no redeeming qualities, as he is not just amoral, but verging upon immoral. He cares nothing for the deaths of people in the novel, particularly Sybil Vane. He goes as far as supporting Dorian's carelessness. From the first time he meets Dorian, Lord Henry seems to be constantly fluttering around him, advocating for his own hedonistic ideals, almost as if he wants to take a piece of Dorian with him.

What makes these characters comparable is that they each develop a compulsive infatuation with Dorian. The reader can clearly sense deeply homoerotic undertones in their dynamics with Dorian. Basil worships Dorian, and Lord Henry does too, but Lord Henry is too full of himself to give himself entirely to Dorian. Therefore, money, class, and their view of morality are the basic differentiating factors between Basil and Lord Henry in relation to Dorian.

In The Picture of Dorian Gray, Basil and Lord Henry have very different relationships with Dorian because they are contrasting characters. Basil's relationship is based on his obsession with Dorian's beauty. This beauty has a practical importance because it enables Basil to develop a new and improved style of art. As such, Basil wants to protect and preserve Dorian and takes it upon himself to be concerned in his welfare. When Lord Henry announces Dorian's engagement in Chapter Six, Basil is concerned that Dorian might marry someone who does not deserve him. This shows that Basil is truly devoted to Dorian and regards himself as a positive influence in his life.

In contrast, Lord Henry's chief concern in life is the pursuit of pleasure and this becomes the defining characteristic of his relationship with Dorian. Initially, Dorian does not know how to interpret Lord Henry and his hedonistic attitude to life:

"Stop!" faltered Dorian Gray, "stop, you bewilder me. I don't know what to say."

Very quickly, however, it becomes clear that Dorian is like a pupil of Lord Henry's, keen to learn the art of hedonism. Unlike Basil, Lord Henry encourages Dorian's dark side, a side which will eventually lead to Dorian's own demise.

Basil Hallward is a talented and kind painter who sees Dorian as a sort of muse, a subject for his paintings who makes him reconsider the way he makes art. Basil maintains an intense emotional investment in Dorian throughout the book, and feels very protective of him- especially against the influence of Lord Henry. Lord Henry is a hedonistic and incredibly charming member of London's upper class who strongly influences Dorian towards a life of seeking pleasure and disregard for morality. He provides Dorian with a book that drastically changes his worldview and a philosophy of seeking new pleasures and experiences.

The two characters are quite different; where Basil is conventional, focused, and extremely protective of Dorian, Lord Henry is pleasure-seeking, radical, and interested in pushing Dorian towards a life of decadence and disregard for conventional morality. Basil is dedicated to protecting his favorite subject, while Lord Henry is determined to introduce him to new experiences, regardless of whether or not they are moral. The major thing they have in common is an intense interest in Dorian, and an investment in his personal decisions.

What contrast does Lord Henry make between Basil and Dorian in The Picture of Dorian Gray?  

Lord Henry says that Basil isn't as handsome as Dorian Gray; he says that Basil looks more like an intellectual while Dorian is a young Narcissus.

While looking at Basil's painting, Lord Henry says:

Don’t flatter yourself, Basil: you are not in the least like him.

He says this because Basil looks at the painting and says that he's put too much of himself in it. Lord Henry misunderstands what Basil means, though. Basil means he's put too much of his hard work, spirit, and care into the painting. Lord Henry takes it to mean that Basil thinks the picture looks like him.

He says that Basil is rugged and dark while Dorian is "made of ivory and rose leaves." He says that he doesn't think a truly beautiful person can be intellectual. In Lord Henry's opinion, a smart person can't have a harmonious face. The one exception, he says, is the church—though he adds that they don't think in the Church. Lord Henry says that Dorian—though he doesn't know his name yet—clearly never thinks.

What contrast does Lord Henry make between Basil and Dorian in The Picture of Dorian Gray?  

In the first chapter of The Picture of Dorian Gray, Lord Henry makes the following contrast between Basil and Dorian:

Basil...with your rugged, strong face and your coal-black hair, and this young Adonis, who looks as if he were made out of ivory and rose-leaves.

To put this into context, this contrast appears after Basil has shown the painting of Dorian to Lord Henry and has told him that he will not exhibit it. Basil explains this by saying, "I have put too much of myself into it," and this prompts the above contrast from Lord Henry. 

Lord Henry interprets Basil's comment as an admission of his perceived beauty. He thinks that Basil believes himself to be as beautiful as Dorian but he is, in fact, making an admission of his love. This reference to homosexual love is one of the reasons why the publication of Dorian Gray sparked such outrage among the Victorian public. Whether Lord Henry really appreciates the extent of Basil's feelings towards Dorian is not made clear in the chapter. It goes a long way, however, in explaining why Basil is so hesitant in allowing Lord Henry and Dorian to meet: he is possessive and protective because he is in love. 

We also learn something important about Dorian in this contrast. Not only is he extremely beautiful, his youth and vitality also strike Lord Henry, hence his comparison to Adonis. These characteristics are what enable Lord Henry to become such a strong influence on Dorian later in the novel and which ultimately bring about Dorian's demise.