65/35 or 7/3 Falco's favor on neutrals. 6/4 Mario's favor on Brinstar. That's about all that matters.
For the most part if your spacing as Falco is decent, Mario can't get in. He can't really challenge B-air or D-air directly for the most part (U-smash does beat them though, Mario should be looking to juggle with this move for damage purposes for this reason and trying to kill with either D-smash or B-throw). Jabs and F-tilt are also hard for Mario to get past. F-smash is super gay for Mario to deal with if you space it correctly because it outranges everything he does including his reverse F-smash and also can be safe on block. Putting Mario above you is really good because he's floaty and easy for Falco to juggle. Kills can be scored by simply edgetrapping intelligently since F-smash and B-air cover everything. B-air edgeguards are also good against Mario's low recovery since you'll probably trade favorably with his Up-B at minimum and then be in a good position to either continue for the kill or edgehog.
Falco overall shouldn't have much trouble dominating the ground and winning from there. Just don't get too predictable with Jab cancels, since Mario can interrupt Jab cancel -> grab with his Jab. Be cautious with Rapid Jabs in case Mario tries to SDI them for a U-air/Up-B punish.
Don't get U-tilted at 9%. Simple enough to avoid, but Mario basically needs to wait until you have about 9% before his U-tilt chains actually combo (keep in mind, Mario can also start U-tilt juggles with U-air at 0). Just shield when Mario Jab cancels you unless you're worried he's going to B-throw kill you at around 160-170%. The only thing Mario can try to combo into out of Jab cancel is Jab, and the link for that is fairly strict. If Mario insists on using D-throw to start combos, just DI away and D-air. Very hard for Mario to punish. What Mario should actually do to try comboing you at low percents is U-throw at 0 and then reading you with either U-air juggles or U-smash. Alternatively if you don't DI, D-throw -> buffered U-smash at 0 hits Falco (you can airdodge, but if you do anything else it combos).
When recovering Mario has fireballs, N-air, and FLUDD mainly to try to mess up Falco. If the Mario is good at aiming fireballs, they can be a nuisance and occasionally mess up SideB recoveries. N-air also can be fairly decent at catching Falco out of SideB occasionally, and its weak hitbox is fairly good for setting up gimps. Not getting gimped or punished heavily by FLUDD is more about having good reaction time and not wasting your jumps poorly, though it can be difficult to avoid if you are forced to expend your midair jump early to survive.
Mario however DOES win the matchup on Brinstar. The platform layout just sucks for Falco, while it's utterly amazing for Mario. Mario can outcamp Falco pretty easily on Brinstar and wait for the lava to put Falco in silly positions. Falco can't really do much to stop Mario from platform camping on that stage just given his jumps are terrible for positioning himself for platform pressure on that stage.