I’d guess that for one thing, Threepio is a likable and useful character, as others have said, and that he’s not obtrusive. Jar Jar, on the other hand…
The racial stereotypes (perceived or otherwise) aside, he’s too obtrusive and smacks of the writers TRYING too hard. Everything he does screams “Look! Look, it’s the comic relief! Isn’t he FUNNY?! ISN’T HE?!”
I’ve heard it said that the one way to make sure a character is NOT funny is to designate said character as comic relief. Too often, a character designed to be comic relief spends too much time telling the audience he’s funny, instead of letting humor grow naturally out of a believable character (as, I believe, Threepio did).
Another illustration of this principle…there were two made-for-TV versions of Dickens’ David Copperfield released within a year of each other, the BBC version that introduced Daniel Radcliff and a TNT version with Sally Field and Michael Richards (all playing things very broadly). The two versions of the character Mr. Micawber are a perfect example…in the BBC version, Bob Hoskins played the character straight, as a sort of Charlie Chaplin figure of dignity in the midst of hardship, and let the humor come naturally and believably out of that. Michael Richards (yes, Kramer) in the TNT version was loud, broad, and had the same “look-how-funny-this-character-is” that plagues the worst kind of “comic relief”.
That’s one of the reasons Jar Jar grates so much. Years ago, when TPM first came out, I used to visit TheForce.Net boards, and someone astutely compared Jar Jar to the Simpsons’ Poochie…a character cynically designed for marketing and kid-appeal, which the audience saw through immediately. I think it’s an apt comparison.
But the interesting thing is…has anyone read the recent book How Star Wars Conquered the Universe? The author, Chris Taylor, details one of the earliest drafts/outlines of TPM. In it, Jar Jar (and his fellow Gungans) speak perfect English, and Jar Jar is a bit buffoonish in places, but overall more dignified and useful. He’s more of a “not-much-book-learning-but-plenty-of-common-sense” type, and helps plead the Naboo’s case to Boss Nass quite articulately (“I have traveled far and seen many wonders, and I have learned that if we don’t become part of this universe, we will die in isolation.”). This first draft wasn’t perfect, but it was arguably better than what we got.
So, Taylor wonders, how did we get from a much more believable character to one of the most reviled ones in SW history? What possessed Lucas to change him? Taylor speculates that Lucas realized the prequels were going to get into some pretty dark territory–the fall of the Republic, the slaughter of the Jedi, the rise of the Empire, the corruption of a good man–and, having become a father himself, worried that it would be too heavy for younger viewers, and sought to lighten it. Unfortunately, he went about it the wrong way.