I said a while back I thought Fox-Falcon is even. I'll give a brief breakdown of how I see the matchup as far as advantages, and maybe there can be an actual discussion in this thread for once. Or everyone can continue to be dumbfounded by any opinion that implies spacies aren't godless killing machines compared to the rest of the cast. Idc, honestly.
Range/Priority: Falcon wins easily.
Disagree, but only to a point. Yes, Falcon's limbs are longer than Fox's and nair & bair are gay. But priority also has to deal with hitbox placement and attack speed, since both are relevant factors in terms of winning exchanges (and contribute to the giant umbrella category that we've labelled "priority"). I could see an argument for pure range but I don't really see the point of breaking down the character traits into comparisons like this and then focusing on such superficial aspects of the trait in a vacuum. It doesn't communicate anything meaningful about the MU or their interaction. But since you did it this way anyway, I'll respond this way.
Also, Fox's bair and u-tilt. They hit in very important areas, particularly when Falcon is cornered. A lot of "beating" Falcon's stuff has to do with out-timing him or out-positioning his hitboxes anyway (with numerous characters) and Fox is perfectly fine at this (at least against modern Falcon play).
Speed: Falcon with a slight edge.
For pure speed, yes. However, a big component of movement is mobility - the ability to maneuver effectively with one's speed. Moreover, speed is a very narrow part of the ground game. It's important, but movement is largely a conduit through which you do your moves. I do have suggestions for you to make this a better argument but... yeah. I dunno. I just don't get what the big deal is from, "Falcon with a slight edge." Fox can catch Falcon and vice versa.
Combos: Both pretty solid, but I think Falcon has the advantage of not having to combo as long as Fox, and him being a fatty can make low %s difficult to work through without grabs.
I agree with Falcon not having to combo for long to go lethal (although stage position matters more for his combos IMHO) but disagree with the low percent thing because grabs at low percent are usually a counter to crouch options and preventing people from combo-breaking out of things with attacks but Falcon sucks at both.
Fox's combos are more consistent than Falcon's because Falcon's combos are reliant heavily on tech chases that he cannot do completely on reaction as a result of shortcomings in his character in order to get the low percent KOs he wants. He has to guess or cover options, whereas Fox can essentially dial-a-combo, force him into the air and then toss moves at him (and it doesn't matter if he's off by a frame or two of stun for a variety of reasons), or reactively tech chase him with a cavalcade of combo moves (including but not limited to u-smash, d-tilt, dash attack, etc). Falcon's answer to non-tech is weak (barring guessing), which prompts a lot of escapable guess games. His throws are also prone to edgecancels and fizzle a lot more than Fox's do, even at very high level. He doesn't have as good a gimp game at the edge either so his conversions into gimps & edgeguards off well-DIed linkers that fizzle (think uair or nair) are a bit weaker than Fox's.
His recovery & combo break options to avoid being further ***** when he gets a chance to escape (or if the combo just ends) are also significantly worse, which facilitates him dying more. Fun.
Power: Falcon wins easily. Fox dying from knees at 60% because he's the 5th lightest character in the game is pretty straight.
This is an incredibly broad, stupid category. Both characters are glass cannons and have no issues breaking crouch cancel, killing the other, or (for the most part) assaulting shields (which is the point of having 'power'). I see no real advantage for Falcon in this regard aside from his ability to spontaneously kill Fox without a setup more easily because he can feasibly toss his knee around as a real strategy - but he can also do that in every MU and it's not like Fox lacks the ability to arbitrarily kill Falcon for no reason either.
Recovery: Fox wins easily for obvious reasons.
Indeed. This is actually very important because not every Falcon combo will end with knee near the edge or at 80%+ and therefore Fox's survival chances can be argued to be better than what you're giving him credit for, even if he's the 5th lightest character in the game.
Edgeguarding: Fox wins easily both because Falcon's recovery is so bad, but also because he has good edgeguarding tools as is.
Indeed. Not going to bother going further with this.
Shield Game: Fox wins easily. He can spotdodge, unlike Falcon. Has shine after wakeup and OoS giving him about a million options to ruin momentum if Falcon drops a combo.
I'm not sure why "shine after wakeup" is listed under shield options but sure. At any rate I am in agreement and there's more reasons why Fox's options are better but this will suffice. You should also make a note about how Falcon's shield is bad vs Fox's pressure.
Trapping at/near the ledge: Fox wins. He can certainly be trapped by Falcon because he has to be cautious of the huge range on uair and Falcon's general ability to dash away, but when Falcon's trapped near the ledge his limited options make him too much on the predictable side. I see trapped Falcon players taking options like jumping at Fox with a knee and praying it trades or if you're S2J, Falcon kicking (and getting away with it every damn time).
Fox's ledge options are way better than Falcon's and you didn't even mention any of his good ones. Falcon Kick is cute. Not much else to say here.
Grabs: Even. Falcon has much more dangerous stuff out of grabs, but it often relies on tech chasing and other less consistent stuff whereas Fox can virtually guarantee a followup, but he's going to kill directly out of a uthrow a lot less than Falcon will out of u/dthrow. At lower percents they seem to have a similar value for setting up combos.
No. Fox will kill Falcon by edgeguarding after he throw combos him. Falcon will do the same, but the consistency of Fox's throw gives him more room to plan his stuff. Comboing Falcon with Fox off u-throw into an edgeguardable position is easy and can be planned much better than Falcon's throw stuff, which requires a lot more improv and (to some degree) guesswork. Moreover, the nature of tech throws gives the defending player more options and unique escape opportunities that are not available nearly as much with high u-throws.
I think a lot of the poor defensive stuff Falcon suffers from is negated more and more the better the players. Top players spend a lot less time shielding than noobs, and even with Fox's great recovery, he is still killed with relative consistency, not to mention he's much more likely to get gimped than Falcon simply because Falcon is too fat to be knocked off stage until higher %s (occasional shine setups are the exception, I guess).
Your opening one and a half sentences work both ways. Falcon can try to shield less and jump to avoid combos and so forth but do you realistically think that Fox lacks answers to this? Lucky mentioned in interview eons ago that you can just nair > grab instead on a lot of defensive plays by Falcon and forgo the shine and it's a very good strat. Moreover, Falcon playing without shield means sacrificing one of his fastest immediate defensive options out of the wakeup and similar situations where he can find himself at frame disadvantage and being smothered in attacks. His lack of a ranged crouch grab a la Marth in conjunction with slow aerials (he can't CC > nair or something like Sheik or Peach) and mediocre normals (aside from gentleman, but that's pretty meh for shaking a Fox anyway) makes it genuinely hard for him to get away.
The consistency of Fox's u-throw is better than the potential to hit the knee lottery with Falcon's throws. Falcon's throws are very good in spite of their inconsistencies but virtually every Falcon has a style of tech option they struggle with because the character is not built to cover everything on reaction. The fact that Fox's throw guarantees you a hit makes it far more reliable and powerful.
I don't think this is a horrible MU for Falcon just because he's fast enough to dance with Fox and protect himself reasonably from the overshoot mixup off movement alone (even if his attacks are slower and his game is more narrow), he has the priority to win exchanges off that, knee at 60% = death is kind of good, weak knee > uair offstage is very good, and he only needs a few links to go his way in a punish order to get the sotck. That said, his inconsistencies as a character pile up vs someone like Fox and Fox just doesn't have those handicaps.