Actually, one of the problems I have with The Cleveland Show is all of Cleveland's friends have a gimmick. Even moreso than Family Guy's circle - there's Peter, then a black guy, a pervert, and a cop in a wheelchair. Joe is the only "gimmicky" one of that group, really - Quagmire, to an extent, but both Peter and Cleveland are fairly "average" characters.
With Cleveland's group, you have the racist redneck, the fast-talking midget, the thickly-accented bear... they seem more like gag characters than actual friends, y'know?
I suppose of all of them, Tim the Bear is closer to Cleveland in that he's the down-to-earth, somewhat slow guy.
...
So, yeah, he's definitely not the Brian of the group.