I'll simply go by my experience on a few match ups before I have to head out again. People usually just chime in with "well it's HugS, not Samus, otherwise Samus gets *****" which is why I refrain from posting any kind of opinions I have on match ups.
Anyways.
I believe Samus has a slight advantage on Falco. It's so hard to describe why some matches are advantageous since there is so much that goes into a match. So in the interest of communication, I'll break the matchup down into 3 crucial categories:
1. Defense
2. Offense
3. Edge game
Samus effectively shuts down Falco's offensive game with her defensive game. I'll assume that the prevention of your opponent's offense is the main purpose of a good defense. Simply put, Samus's upB out of shield stops most any effective approach Falco has in any other match up. The Falco can only hope to be able to trick the samus into mis-timing or mis-using her upB. These are artificial ways of dealing with the situation IMO, as tricks run thin. You can play rock paper scissors with a good samus and hope she can't figure out when you're grabbing/attacking. Any attack will be beaten.
If you do manage to get that first hit in, Samus has her passive defense, which involves her inability to be combo'd very well. Not that it's flawless, but it helps make this portion of the match up go into her favor.
Defense Adavntage - Samus
Offense - Clearly, falco has a better offense. He can overwhelm most any character. Samus's offense isn't the greatest, but it's better than Falco's defense. And if Falco's Defense has 1 purpose, it's to stop Samus's offense, and it won't be able to do that. Missiles aid in the approach, and once Samus is in there, it becomes a matter of outranging Falco and being able to quickly switch to defensive mode if needed. The main factor that puts this slightly in Samus's favor (IMO) is falco's ability to be combo'd. Which means that Samus need break through falco's defense only once to possibly end his stock. And if the falco is camping, Samus can close in with missiles, break through lasers with a wavedash - tilt and catch falco only once to tie up the damage, or take the stock. This is all hard, mind you, which is why most people don't even consider this an advantage for Samus. Either way, it's only a slight advantage to either no matter how you look at it.
Offense - Slight Advantage for either Falco/Samus,
3. Edge Game - It's no surprise that falco has a shoddy recovery. It's also no surprise that Samus has one of the best. So this part of the Edgegame clearly goes to Samus.
As far as edgeguarding goes, that requires some analysis. I'd have to give Samus the advantage on this one. Samus has an amazing edgeguard coupled with the fact that Falco has a terrible recovery. Limiting his options is cake. If he side-B's, ftilt. If he up B's from below, utilt. If you don't know where he's going, shoot a missile/shot to make him go where you want, then commence with the process. Falco on the other hand, must keep track of all her options. First he must get rid of the grapple, then he must stop a sweet spot, which ain't gonna happen if the Samus sweetspots perfectly. And if the falco grabs the ledge, you should still have your jump to get in anyways. This on top of the fact that's there's no distance samus can't come back from means that Samus doesn't die from falco edgeguards.
3. Advantage - Samus
So I hope that helps explain why I feel Samus has the slight advantage over falco. I don't have more time to write about other characters atm. And I could probably delve into Samus vs Falco even more, but I think this is enough.
And FYI Fletch, your sig is dumb. You can employ patient thinking/predicting in checkers or chess, the main difference between the two games is the amount of options, and chess, like Melee, most definitely delivers more options.