Falco doesn't have to kill Snake to win. He is quick enough to circle camp Snake on certain levels and with an early lead of either a stock from a Spike off of CG, or 75% damage from C-grab to Dacas and a bit of lasers, well.... Sure he may not kill Snake easily, but he mounts damage incredibly quick. More so, between Phantasm, his incredible Spot dodge [only 3 frames where he can be hit], his fast fall speed with an average air dodge, he can be rather annoying to catch.
Once Falco realizes that he has the lead, he can rely on his defensive options to easily punish Snake. Good Falcos will almost universally utilize Jab [Frame 2]/Shield to grab once they have a lead with the rare F-Tilt [Frame 6]. They'll then throw the opponent off the edge, to respace, or attempt to mount a kill with a bair/dair, or the rare Uair. With his horizontal control of the level through his Laser Game, it reduces the efficiency of Snake's projectile game significantly.
The match dynamics change drastically pending on who has the first stock taken from them. If Snake is attempting to advance with his nade game, it typically is shut down, but if he's attempting to be defensive against Falco with them, it keeps it's traditional effectiveness. While, as mentioned before, Falco has a tremendous ability to control horizontal space, operate out of shield, and generally avoid being in an area where he'll take damage. But, if Falco is approaching it is relatively clear what he's going for at all times [jab and throw set ups.]
This match up snowballs quickly, for either side. Falco has a massive early game edge, and if he plays it as if the first stock is the match is the last one it can make it incredibly hard for Snake to catch up. Though Snake is 'hard' to kill, Falco is going to be dishing out either a Vertical Kill move, or he's going to be edge guarding you with either a dair [small area of edge, easy to avoid], or read your air dodge [or lack of] with a bair/uair which will kill in the early hundreds.
So with all of that said, both characters are actually relatively similar in their style of play. Both are punishment oriented characters. If Snake wants to win, he needs to avoid the easiest punishment in the game... A grab.