Mario's f-smash is clearly better, it allows you whiff punish anything with a kill move from a pivot, which is great in all matchups. Doc just gets very little opportunity to hit with such tiny hitbox and long startup. He has a strong downsmash that is much faster and has pretty good KO power too, I use this instead. I can only really hit people Doc's f-smash if I run through them and pivot and hope they whiffed a grab or try and WD.
Mario's up-tilt is both underrated and overrated. It stops aerial approaches and can start combos unlike Doc's which only pops them up if you hit at the tail end of the animation when they're right above you. However, as Mario you want to be hitting them at the end of the animation anyway, as hitting early in the animation means you have more recovery frames to go while their hitstun dwindles away. So Mario's advantage here, which is only for non-tipped utilts, isn't much since Mario's non-tipped uptilts are kinda mediocre anyway. HOWEVER as combo filler, Mario's utilt does help since you don't have to be as precise as with Doc -- almost-tipped utilts work just fine whereas Doc's don't. But... Doc doesn't have to utilt for combo. He has his weak upsmash and up-B glitch.
Mario's jab string is better, but not by much. Both strings can be crouch cancelled and punished, and for both of them on hit, it's better to go for a not-usually-guaranteed-but-works followup like grab or downsmash anyway. Doc's's jab-dsmash is better since his downsmash is better. But, Doc's jab string can be shieldgrabbed whether he does the second hit or not, whereas Mario can delay his second jab and interrupt punish attempts.
Mario's nair is better, period. Doc's late nair has smaller hitboxes and just doesn't hit very often. With Mario you can actually approach with rising Sh nairs by crossing over them, while catching their SHFFL aerials, and actually have options after it hits. With Doc it's so weak that you could be punished for hitting it too early in the jump and you can't approach the same way. But eh nair approach isn't that could anyway. Why approach with Doc when you can just pill and bair wall of pain? Nair as a combo ender is pretty good too in comparison to what Doc has as an aerial ender -- is reverse bair comparable? idk
Mario's dair is better, and the fact that his fastest aerial nair is stronger makes dair even more useful. I don't really find much opportunity to use it though, but I guess it's still better than Doc's. I never use Doc's dair unless I really need good hitboxes below me. Maybe GreenMario's use of dair and that platform autocancelling trick would change my mind, but this isn't much of an advantage over Doc.
Mario's fair beats obvious crouch cancelling a bit better than doc's does, since meteors counter ccing, but Doc's fair isn't far behind since it also hits really hard.
Thing is Doc has a bunch of other things going for him that put him ahead. The reality is, this game is about taking stocks, not just doing damage, and Doc closes out his stocks better while having a comparable combo game (yes he does).
Doc has up throw fair on fastfallers. Both Mario and Doc have dthrow dsmash, with Mario having fsmash available at higher percents with side DI and Doc having super-powerful fsmash with no DI. Mario really isn't that far behind here.
Doc's bair gimps earlier than Mario's does. Yes, j3lly says Mario's does it too, but Doc's does it at earlier %. Also is it just me or does Doc's bair spam make a more impenetrable wall than Mario's does? It seems to have a longer hitbox and SH bair autocancels are uninterruptable on hit and command more respect than Mario's bair does. But Mario's bair has other uses though so again he's not far behind here.
Doc's pills are better than Mario's fireball. Both characters can FH pill/fireball waveland, but Mario's fireball waveland is good in a tighter window than Doc's due its speed. Mario can camp and actually do damage because they're decently hard to react to at a certain range, but Doc's pills control space a lot better and has a better angle for more situations. FH pills counter projectiles better than FH fireballs because with pills you can jump over missles and lasers at close enough proximity where they can't dodge the pill very easily. Try that with fireballs and you'll either be too close and the fireball will just go past them or you'll be too far away and they have enough time to neutralize the projectile easily. There's also Doc's ability to put multiple pills in the same general area which Mario just can't do.
Doc can go lower in his edgeguards than Mario can, since his vertical recovery is higher. Pill edgeguard hits at better angles against most characters whose max recovery distances involve moving at 45 degree angles. J3lly may say that Doc's bair isn't that much better since Mario can just bair-bair instead, but you can't always link the two due to the position Mario might put himself in, since it's dangerous to go very low as Mario.
Doc's d-smash hits noticeably harder, which makes his crouch-cancel punishes better and his jab-dsmash better.
Doc's dtilt actually has a use, which is sending your opponent behind you. May seem dumb, but reversing positions when you're cornered by the edge with a move you can do from a crouch cancel can be quite the stratagem when you consider Doc's gimping abilities with bair (you're already backturned after dtilt hits, too!).
Doc has the up-B glitch, which is the reason I play Doc over Mario now. Mario has nothing compared to this. It greatly improves his defense against shield pressure and it is great in combos. With it, he can link combos in ways that Mario can't. It's a 3 frame move that hits in front of him that you can dash into and combo out of and into, so this plugs countless holes in the Marios' combos. Want to be able to combo into and out of Mario's utilt from the ground but can't because you're Doc? Just Up-B glitch instead. It'll link out of every attack that jab would since it's a 3 frame move. Jab cancel jab works? So will jab Up-B glitch.
Mario's combo game really isn't better when you factor in the up-B glitch. This isn't just in theory either, Up-B glitch is really easy to when it there's a hitbox, since it adds hit/shieldlag that gives you more time to hit the back direction to cancel it. Along with u-smash, Doc's is more than compensated for his lack of up-hitting non-tipped utilts.
So in conclusion, Doc's advantages over Mario has real meaningful value in competitive play where Mario's advantages aren't real game-changers with the exception of his fsmash range. Doc does better against the top tier and ever-popular fast-fallers and I think Mario does better against Peach/Samus/Puff due to f-smash and fair beating their crouch cancel.