Vincent Alexander, commenting at Michael Barrier's site, disputes the idea that Bugs Bunny is fundamentally two different characters in the hands of Chuck Jones and Bob Clampett. Though I've always been a bit of a Clampett-skeptic when it comes to his handling of Bugs, I think he makes some very good points.
I'll add that this may be one area where children are wiser than adults. Children (and I include myself as a child) never have any doubt that Bugs Bunny is the same Bugs Bunny in all the cartoons, whether he's fighting back after provocation or having a good time heckling Red Hot Ryder. It's all the same guy, doing different things. Whereas kids do understand, instinctively, that the Daffy Duck of "Show Biz Bugs" is a different character from the Daffy of "Yankee Doodle Daffy," even though they're both obnoxious guys who want to get ahead in show business. I remember as a child seeing Clampett's "Draftee Daffy" and thinking that that was a bit more like the Daffy I was used to. I was confused, at the time, by the early Daffy -- but I was never confused by any incarnation of Bugs.
Speaking of "the same," Thad posts a Fox and Crow comic book story that has the same story as Chuck Jones' the Daffy Duck cartoon "A Pest in the House." The comparison is interesting because "A Pest In the House" is just better, even though it's a similar story by (presumably) the same writer. It's not just that Daffy's behavior is less hateful than the crow's, and it's not just the animation and music and voice acting; even just as a story, the cartoon has a better structure, a better use of the running gag, better ending, better everything, really. It's a reminder of how a good director can get better work out of even great screenwriters.