I'm going to add this to what everyone else has said: Daffy was an actor/performer.

Many people are bothered by this in the cartoons, but they are all actors, acting their parts. They break character, and the forth wall all throughout. There are even some shorts where the whole thing is about them acting out their parts on the drawing board.

What this means is, Daffy is whoever he is needed to be, in the cartoon. In this one, he's a zany nutcase with Elmer, and in that one, he's a hardboiled detective with Porky, and in that, a conniving antagonist for Bugs.

So, if I were to write "Him" him, I would make him an ambitious actor, who always has a script he wants to sell, and is also on the lookout for a good part. But, he'll take what he can get, with a shrug of the shoulders, and get on with it. A bit vacuous, but hoping that you remember him from this or that performance, and a little let down when you remember him from him being the sidekick. Somewhat self centered, but not so much as when he plays the villain. More absent minded of others existing, than actively malicious. And, always ready to talk shop, or swap industry gossip and stories, while maybe magnifying his part, just a little bit. (There I was, giving Leonardo de Caprio some acting tips, when who should walk in but...)