What is the difference between how Miles and Jesse view their immortality?

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"Maybe. But we don't know them," Jesse pointed out. "We've never had anyone but us to talk about it to. Winnie—isn't it peculiar? And kind of wonderful? Just think of all the things we've seen in the world! All the things we're going to see!"

"That kind of talk'll make her want to rush back and drink a gallon of the stuff," warned Miles. "There's a whole lot more to it than Jesse Tuck's good times, you know."

"Oh, stuff," said Jesse with a shrug. "We might as well enjoy it, long as we can't change it. You don't have to be such a parson all the time."

"I'm not being a parson," said Miles. "I just think you ought to take it more serious."

The above exchange happens between Miles Tuck and Jesse Tuck in chapter 8.  They have just finished explaining to Winnie Foster that the fresh water spring in the Foster woods granted them eternal life almost a century earlier.  Miles and Jesse Tuck have polar opposite opinions on the ramifications of eternal life.  Miles Tuck sees his eternal life as a big responsibility.  He sees it as something to be taken care of carefully and used as a tool.  

"Someday," said Miles, "I'll find a way to do something important."

Jesse, on the other hand, sees his eternal life as a way to extend his fun and enjoyment of life indefinitely.  Jesse's eternal life isn't so much a tool to be used (as it is to Miles) as it is a toy to be played with.  He plans to use his eternal life for perpetual fun.  It's important to note that Jesse is the only Tuck family member that sees eternal life in this fashion.  He's also the only Tuck family member that encourages Winnie to consider drinking from the spring at some point in her life.