i was just about to post this
Carlton was about that life...brought the burna into the hospital on some g-shyt

And Will was running, like Usain Bolt, from fist fights.
But, Will is realer...
Both had moments of disrespecting each other throughout the show (Will on Carlton's level of blackness, Carlton on Will's intelligence). Also, Carlton had inferiority issues in relation to Will. For some reason, he could not handle Will being better than him at certain things, nor could he handle the fact that Will was more popular amongst their peers. Remember how he acted when Will joined the basketball team, or when Will had a higher SAT score?
Both had their growing pains. Carlton was the only boy, in the house. And here comes this tall, smooth talking, handsome, athletic guy to live in. Of course, like all us men do, he tried to find a place where he excelled.
And you said it yourself; Will's beef was Carlton's "blackness," but, Carlton had beef with his intelligence. I'd have to side with Carlton as intelligence has more to do with success, than being cool.
Yes, Carlton assumed Will was a savage because he came from the hood. But, I blame that on being sheltered and let's not pretend Will didn't play up his weight back in the streets of Philly.
Even Aunt Viv called Will out; he wanted ppl to stop tellin' him to change and judging him, but, he did the same thing to Carlton.
Carlton called Will out for being just as bad as his Dad (in the later seasons) and Will hadn't done much to prove him wrong.
Nothing wrong with being from the hood. But, when you've got a rich uncle willing to support you, actin' hood, in Bel-Air is plain foolish. That's Will's problem. He was smart, but, wanted to hustle and charm his way through life, like he didn't live in a 8 room mansion and had a judge for a father figure.

And it ain't like Will held weight in the hood. He got exposed when they went back and even ol' ladies was laughing at him.
Of course Carlton was shook, he was from Bel-Air (lived in the hood for a short time), but, at least he didn't front like he was thoro' because his fam' spent a short time (during his life) in the hood, before Uncle Phil made it big as a lawyer.
Will was tryna front like he was Nino Brown back in Philly and Jazz was prolly harder than him

, in Cali.
Again, Will was the one fronting and it bit him, later on.
He still couldn't find an apartment, at the series finale--didn't want to take the job with Hilary, in NY. Like he couldn't have turned that into a career in entertainment.
Will made bad decisions all throughout the show.