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Mario's biggest assets are his great mobility, his weight, a reliable projectile, a great out of shield game and his strong combo game. In neutral, you need to play in mid range a lot of bait out Mario's approaches. A majority of his aerials are very difficult to punish and all but two of his moves come out faster than frame 10. That's pretty ridiculous in itself. Playing in close range is really risky because Mario wants to grab you. Mario can reliably combo us well past mid percents. Up-Tilt combos don't really work as well here because below 10% or so we have enough time to shield or take another action. There is also the chance that due to our lightweight, we can jump out his string as well. Getting grabbed though, is really bad. Up-Tilts from Down Throw past 10-20 or so can lead to multiple Up Airs followed by a Super Jump Punch for additional damage. You're always in danger of being comboed reliably until like 90-100 or so but you'll want to take extra precaution to not let Mario get additional damage on you. Although Mario's Up Air is a pretty solid, Dair camping helps a lot here. Our ground speed is also going to be a big asset for punishing Mario. It's basically a lot baiting and switching between air to ground to create openings. It's a tricky matchup.
The other thing you need to watch out for in close range is his Jab. It's fast and it will pretty much beat out anything we'll want to do close range on the ground. You're better off resetting if you end up having to engage a grounded Mario while on the ground in neutral.
Fireballs are useful to Mario if he isn't spamming them mindlessly. If they get careless and we're close enough we get a free Mach Tornado. Drill Rush can be also be used for eating Fireball but the range where you'd want to use Drill Rush is the range where Mario has enough time to take an action and punish you for it. If Mario ever uses Fireball in the air from a full hop and you're close by, you can just aerial through it. Nair, Fair or Bair all work well. Mario is safest with Fireballs when short hopping them, using them infrequently, or using them at longer ranges.
Mario's aerial approaches are something to look out for as well. Dair links into all sorts of dumb stuff depending on the percents and that includes grabs and smashes. It's also has very little end lag and is difficult to punish on reaction even if you powershield it . Many Marios like to cross up your shield with this move so pay attention to that. Bair is also pretty good for spacing as its got nice range and it's fast. The brightside here is that our F-Tilt is really useful for zoning Mario's aerial approaches. Bair is still telegraphed and Mario's range in general is pretty bad. Our F-Smash is also really nice in this MU. It's actually difficult for Mario to punish it because of his lack of range. I use this move a little more liberally in this MU. Very helpful.
Respect Mario's out of shield game. Up Smash is a stupid move. Fast, powerful, hits quite far behind him (good Marios will Jump Cancel Pivot Up Smash for optimized punishes). Do not challenge this move, like ever. If you think it's coming, wait for it in mind range and DA/Dash Grab him instead. Also, you can expect Super Jump Punch if the Mario is trying to go for something faster. It's Frame 3 and has invincibility on it.
Our combo game on Mario works well and the fact that we combo reliably for longer than he does is a large part of why we keep up with him. Optimizing punishes on him is key since he's fat as well. Make sure you are precise with your combos as Mario can punish you with Nair or Super Jump Punch if you miss your timing. Alternatively, at low percents, you can bait out those and punish him for that.
Edgeguarding here is pretty weird. It's really hard for both sides to actually gimp each other but if one side messes up, that's a stock. On one hand, its actually hard to gimp Mario if they save their second jump and only use it when they have to. On the other hand, it is possible and you manage to hit him out his second jump, he's pretty much dead. You can sometimes catch them with F-Smash on the ledge as they Super Jump Punch back to the ledge. The move comes out on Frame 3 but the invincibility comes out on Frame 4. Keep that in mind. If you go off stage and chase directly, you'll rarely get anything substantial because they can just go through you with SJP. If you're going to try to actually go off stage and gimp, do it asap. If you want, you might as well just play the ledge game and see what they're going to do. If they recover high and use Fireball to cover themselves and you're close enough, you can easily go through the Fireball with an aerial or Nado and possibly kill them. I see this move as a mixup but it happens.
On the flip side, we have to be careful. If we mixup how we recover, we're fine. If ever get predictable, it can get bad. Tornado will get you Caped and/or FLUDDed easily if you're dumb with it. Same with Drill Rush. Shuttle Loop and Dimensional Cape are safest but Mario can hit you out of either with Nair due to how long the move lasts. Keep in mind this is a commitment so you're fine if you bait or if they miss with it. But basically, don't recover in the same way too many times or that's your stock. Mario can totally Cape you out of Shuttle Loop also. Other than that you should be fine. But do keep in mind something: Mario can sometimes DA at the ledge and its long lasting enough to go through your ledge invincibility and semi spike you from the ledge. It puts you in the a really bad position, even for Metaknight.
Basically, I just play really patient and bait out what Mario does. I treat this MU like Luigi except the punishment isn't as bad but Mario can actually constantly pressure and chase you due to his mobility. He's fat, so that is a something to take into consideration. He's got a nice, expansive combo game, and he's one of the few characters that can just outright kill us off stage if we make a mistake. And his moveset is overall faster. We have a better combo game, a zoning game, better range and we're more competent off stage. The range factor helps quite a bit because we get to play out of shield more because of Mario's poor range. That means you'll have an easier time getting those shield grabs and Loops. I also tend to land more Up-Smashes here than against most other characters for this reason. Both characters shine in many of the same categories but have some key differences.
Overall, I feel like it's a pretty even MU. I can maybe see the argument for 55:45 MU but I totally disagree with anything more than that. I still think it's 50-50 as of now. I play this MU with a very competent Mario, all the time.
EDIT: Random tidbit: Watch out for FLUDD. Specifically, if Mario ever reaches full charge with FLUDD, there is zero cooldown from that charge state. Some Marios will continue a charging from a partially charge FLUDD in an attempt to bait you and punish you because they act immediately after.