I disagree with the views expressed in the thread so far.
I think there is a legitimate case to be made for Falco when someone asks which Star Fox character they should play. Each has their own advantages and disadvantages that doesn't just boil down to suspect matchup charts.
Fox is the fastest of the three. He does not have lasers with hitstun so neutral is not as easy as Fox as it is as Falco and Wolf. However, Fox has far more options in neutral than the other two. Everything Falco or Wolf can do when approaching, Fox can do that and more. He can nair, dash dances, waveland on and off platforms, plus run straight pass the opponent and pivot with a move. He can waveshine, dair multi-shine on shield, laser camp to force approaches, and so on. His up-smash out of dash also has no equal.
Fox doesn't have as extensive a punish game as Falco or Wolf, nor quite as many options in his punish game, but what simple options he does have are terribly effective, like upsmash, upair, or Reflector. Fox also has the longest recovery of the three, I believe. He falls the slowest and is the lightest so he is less resistant to being vertically KO'd himself. Fox gives floaty and slow characters a really hard time because of his vertical killpower and his ability to react to their moves while they are unable to react to his moves.
If you like to look cool in neutral, and you don't care a whole lot about the punish game, then you'd maybe pick Fox.
Wolf, briefly, has just about as long a recovery as Fox, but far more vertical survivability. His neutral game is stupid easy because of waveland blasters which many players have no idea how to deal with, and many characters lack native options to deal with; and so he steamrolls people in neutral. His punish game is also the most extensive and versatile of the three; his Reflector and up-air and Wolf Flash figure greatly into that punish game, and his ability to pull off long flashy combos is part of what draws players to Wolf. But Wolf at his best is highly technically demanding and risky, as many kills by top players are earned via Wolf Flash, sometimes off stage, sometimes on-stage; a miss either spells death or the beginning of a devastating whiff punish.
As for Falco, I'd say he's almost the best of both worlds. You get to have a good number of options in neutral, though not as many as Fox, nor as dominant as Wolf's, and a solid punish game, though not as devastating as Fox's nor as "cool" or damaging as Wolf's. Falco is a balance between the two still with his own strengths that unfortunately go under the radar. He has the highest jump, the most dangerous recovery for the opponent to edgeguard, and, I'd say, Falco is the least technically demanding. SHFFL is not as hard as waveland blaster nor Fox's short hop double laser you can see the CPU perform, and although you can move like Fox does to a certain extent, because of Falco's laser, you aren't exactly obligated to.
Falco has a plethora of powerful and useful moves, though they are tough to follow up into, like fsmash, dtilt, and Fire Bird off the top. His lasers and dair also give Falco a great edgeguarding ability.
There's a lot to be said about the differences between the Star Fox characters but I think ultimately, there are sensible reasons to pick each one of them, and none of them are strictly better than the other.