i still think fox wins the matchup, but it's close
the way i see it, fox is better at spacing and poking, but falco has a better punishment game
Falco's shine is ******** good, once it hits. Nobody disputes this; falco's shine forms the basis of his punishment game. He sends you up, he kicks you down. He sends you up again, jumps on a platform, sends you up, you die, etc. His combos are super damaging, demoralizing, and they usually lead into an edgeguard. They're extremely hard to SDI out of, and even then there are variations to counter this; nair instead of dair again, upair/upsmash after a shine, bair to carry you out over the edge, and so on.
Fox has a great punish game, but it's not as good as falco's. You get a grab, and you upthrow. Depending on percent, you follow his DI for the upsmash (or do a standing upsmash, if they're too low to DI). Then you have to run to where he lands, and react to the tech--if he techs in place or misses, you get another upsmash or grab, forwards or backwards you need to dash in their direction and do another jc upsmash. Then the option tree gets bogger, depending on platforms and their DI. On FD, you can do a full-hop bair or nair (or two, if you start from the middle of the stage). On smaller stages like Yoshi's story, they're probably out over the edge, so you switch to edgeguarding. On dreamland or battlefield, you might have sent them up to a platform, which has its own way to follow up.
For fox, I feel like once you get the opening, you need to move QUICK to maximize your punishment. Most of fox's nasty combos you see on youtube have at least 2 or 3 clutch instances of tech chasing in them. You need to harness control of the match if you want to punish as hard as you possibly can; you need to scare falco into going where you want, then react extremely well. That's the only way he matches falco's punishment game. Once falco lands a shine, the control of the match just gets handed to him on a silver platter. Most importantly, you can combo fox WITHOUT giving him any chances to escape. It's more "guaranteed," in a street-fighter sense. I feel that he doesn't have to work as hard to keep the combo going.
(The only exception would be FD, since the option trees are comparably simple, and getting chaingrabbed sucks.)
Fox wins the movement game, though.
He's got a faster dash speed, which helps a LOT. If you look at the individual moves that Peepee/Jman use to maneuver and space, Peepee has to work more. He constantly dashes into a wavedash, since that's the only way to move as fast as he wants in certain situations. Fox can "get by" with just dash-dancing. When you crank up the speed of the match, all the way up to cracked-out pro level playing, Fox has more tools to space faster. The mobility advantage he has over falco makes it easier.
But what about lasers? Don't they cut off options/**** fox/control the stage?
If you space correctly vs falco, you never give him the chance to shoot a laser. If fox is right there, either hovering in the air above falco from a fullhop, or waiting just outside falco's bair/nair/grab range, Falco can't shoot a laser without putting himself in danger. If falco short hops into the air to go for a laser, fox can rush in with a nair to stuff his face. He shines after, and gets control of the match. If fox is in the air, in his wonderful, amazing, viable full hop, he can react to a poorly spaced laser and punish with any aerial (and drill to beat crouch canceling). Same goes for platforms; fox can punish with a drop thru bair, or fullhop from a platform and react to a bad laser. Lasers just don't seem like that big of a problem to me; the real trouble comes when falco wins every exchange when you try to approach, but that's a different skill altogether.
Falco is great at keeping fox out, but once fox is in, he's there to stay.
SHLs are great at keeping fox away, but that's it. After you get sent to the other side of the stage (say, from a forward smash at mid %), you need to deal with 3 or 4 lasers before you can get back up in falco's face. Both characters can play *****y and make it hard for the other to approach; I'd say falco is slightly better at this, but the difference is negligible. Fox's shine OOS is awesome at swatting falco away again and again. Both characters have a lot of tools to piss each other off. They tie at playing campy, since they're both good at it. Falco's lasers and fox's fast OOS game balance out, imo.
Once fox is in the space he wants to be at, he really has the upper hand. If fox catches falco doing something he shouldn't, he approaches for free. Any bad laser and he gets in (like I described earlier). Basically, if falco throws out any move, fox can come in with his super sick dash speed.
Once he's in, fox has a clear advantage. I think that a lot of foxes play the matchup dumb in close quarters, and they shield pressure just to hit falco's shield because they like the feeling, or something. It's too risky (and dumb) to try to nair on top of falco over and over; shine OOS will **** you. Switch your perspective from "hit this bird's shield as many times as possible" to "land as many SAFE hits as possible, and be ready to move after one hits to follow up." Whenever it feels like I'm shield pressuring right, it's because I'm trying to poke effectively, over and over. Fox's bair outranges all of falco's moves. If you use them in the right situations, nair and downtilt are totally safe, too. If you're in hot water, you can cover your bases with a shine. There is almost always a way to hit falco's shield and be totally safe afterwards.
As a comparison:
Falco's shield pressure is harder to pull off, since he's not as fast; it's higher risk, higher reward. Fox has a quicker shine OOS, and a better upsmash OOS, so he can get falco off of his shield easier. If he messes up though, falco will land a shine and get a huge punish off of it.
Fox, on the other hand, has a lot of safe ways to hit Falco's shield, and since he's got faster movement speed, he can space himself easier than falco can. If you stay in the right space, Fox gets a lot more free, safe hits on shield. And, if you're smart about it, you shouldn't be punished for any of these. Try to land a poke, and then put yourself in the space that falco wants. Fox has an easier time of this, since he's got faster movement speed.
tl;dr
fox has a slight advantage when it comes to movement, following up, and approaching. falco has a notable advantage when it comes to punishing, since his shine combos are more guaranteed. fox has an advantage in the shield pressure game, but only if you're smart about it. shield pressuring like a dummy will get you punished quick, and falco's got the better punishment game.
:D
this post took me like 2 hours lol
those are my thoughts
i feel like the matchup really boils down to those things, and fox has a slight advantage that he can push all game. i'd call it 55-45 for fox.
