Milan were the greatest club in the world from 1989 to 1995. That was a purple patch, a golden era. Inter have never matched that - but then again only a handful of clubs (Real Madrid, Ajax, Bayern, Liverpool, and Barcelona) ever have. Even Juventus - the most successful Italian club bar none - haven't, and nobody would really argue that Milan are bigger than Juventus. Thing is, when you are the size of Milan or Inter, that question is pretty redundant. It's like asking which of Real Madrid or Barcelona is bigger? I mean, Real are the greatest club on the planet - but does it actually mean anything in a head to head with a club the size of Barcelona?
In Italy, it is Juventus versus Inter that is the Derby of Italy. Juve, Inter, Milan...all pretty interchangeable.
Regarding Ballon d'Ors, Milan have had more wins by players in their shirts - but both have also had Ballon d'Or winners in their shirts who had already won that title at other clubs. So it's not the perfect metric for saying which club had more great players. I mean, Rummenigge won as many Ballons d'Or as Gullit and Kaka combined - but at Bayern. There is no doubt that since the late 1980s, Milan have been the more successful club: 9 Series A and 5 European Cups. Inter have 7 and 1, by comparison.
But both are mega clubs.