The Elven change in character

[The Saucepan Man]

I don't see a problem here. Descriptions of a given individual or group of individuals can vary widely depending upon what they are doing at the time and who is doing the describing,as well as a range of other factors.

If three different people each sat down to write their impressions of the Saucepan Man, one when he was in the pub with his mates, another when he was at work and a third when he was playing with his children, I am sure that they would come up with some quite different and possibly contrasting descriptions.

[Kitanna]

When I first read The Hobbit my impression of the elves was that they were crazy pixies (or something of the like) hiding in the forest. Then with LOTR that all changed. It was Lalwendë who made the point that the elves could be more happy and carefree because there wasn't really much of a threat hanging over them. It goes the same for people, at one point in their life they can have fun and be carefree when some time later they are serious, then they can go back to being carefree later on.
So though the elves are happy-go-lucky and teasing of the dwarves in The Hobbit they, like many people, put that attitude away when something serious happens and it needs fixing.

[Formendacil]

It's a matter of protagonist as much as anything else, I think. Bilbo vs. Frodo. And no, I am not talking about the translator conceit.

In The Hobbit, we follow Bilbo. We follow his adventures and his tales. As such, the Elves that we see are the ones that are most likely to make contact with him. In general, those are the happier, more carefree ones. Remember, Bilbo is just a hobbit burglar, a curiosity in which silly elflings, and not great elf-lords, would be likely to place an interest in. In addition, Bilbo's own preference for Elven company seems to lean more to the "tril-lil-lil-lalliers" than to the Glorfindel bunch.

In the Lord of the Rings, by way of contrast, our protagonist carries the greatest trinket in middle-earth. What he does will decide history for millennia. Quite naturally, as we follow his journey, we are going to see quite a few more serious elf-lords than we will dancing elflings. In addition, Frodo's character is such that he gravitates more to the solemn and wise than Bilbo did. (Even in his old age, Bilbo keeps the company of Lindir and such, as well as more rogueish sorts like the Dunadan).