Well, Caine is sort of like Henry Hill in Goodfellas, because he is the narrator and sort of "cool" member of the gang

O-Dogg is like Joe Pesci's character Tommy, in the fact that he is violent and crazy

A-Wax is kinda like De Niro's character Jimmy, because he's the older wiser one

The scene where O-Dogg shoots the base head and A-Wax is upset is kinda like the one in Goodfellas when Tommy shoots Spider and Jimmy is upset

And the steady cam scenes

Plus in the Goodfellas SE DVD The Hughes Brothers said they based Menace II Society on Goodfellas or something