As far as doing good/better than Mario, you could say to some extent Ness as his projectile works decently vs. him but I lack the experience in that MU in particular so I can't positively say it, but none of Doc's projectiles can be absorbed by Ness giving him actual control to SOME DEGREE in that MU. They're more effective than Mario fireballs in that MU at least. Anything else I'm not sure, but I do think Luigi is thankfully relevant cause he's a common pick right now and I think it's important to note.
I think the only top/high tier MUs that I think Doc does notably bad vs. are Sheik, ZSS to some extent, Rosalina a bit, and Pikachu off the top of my head. Everything else is just slightly worse than Mario MU IMO, but this could change down the road (I'm far from perfect lol).
Diddy actually isn't horrible (not great either but not hardcore loss) and Luigi is alright to deal with as Doc. Falcon I argue is close because of Falcon's options vs. Doc's and how they punish each other so far (really fun MU).