It's hard to say exactly. I'm not that great with words and my opinion on this comes from maining both characters, and entering tons of tournaments over the years, as well as from playing countless friendlies with StriCNYN3 each month in this exact match up.
I think the main thing is though, that because he is so fast and mobile as long as the fox is patient enough and is good at foresight and positioning and taking a laser or two he always gets to eventually dictate the actual inevitable engagement after the positioning battle is said and done vs falco (and any character expect maybe captain falcon who is slightly better than fox, but we all know falcon blows). What I mean by that is the combination of his jump speed, dash speed, and just overall maneuverability is going to allow him to play the positional game long enough to where eventually a skilled fox is going to come in at an angle of his choosing with the advantage.
No other character has that luxury. Falco's positional game is strong indeed with lasers and what not, but there are situations and characters who can force falco to take risks and force him to come in at an disadvantage.
Sorry, that's the best I can explain it. If that's not good enough you'll just have to take my word on it. Also because of fox's jump speed and shine range both being better than falco's his pressure game is more air tight too. It's nearly impossible or impossible to shine out of shield vs perfect fox pressure with nair shines or something, and it's really easy even with skilled falco's to shine out of shield combos for me on them unless they do SUPER low ariel attacks.
Fox is just also better at teams, on weird stages, and just in general as well.
I realize falco has his advantages like he's heavier so he dies slower, and can CC stuff at higher percents, and much more i'm not mentioning, but imo melee comes down to that back and forth posturing position and the eventual engagement more than anything else, which IMO fox dominates at in the majority of the match ups compared to other characters, he's just so fast and flexible with nearly limitless options if your good enough.