Falcon's DownB >>>>> Mario's DownB. That's pretty much it for things he's better than Mario at.
If you want a really fun character and someone who everyone at tourneys will root for, go with Falcon. If you want someone who's pretty fun and has a much better chance of WINNING a tourney, go with Mario.
I main Mario/G&W, and secondary Falcon (among a number of other guys), but I honestly think Mario's FLUDD is more useful than a Falcon Kick.
Mario's FLUDD is something that keeps him unpredictable and able to ledgeguard better than most characters. When ledgeguarding,
it stops people from grabbing the ledge which gives you a good window to punish recovery with something else (and successfully Caping people is literally just as effective in Brawl as it is in Melee). The pushback occasionally gimps recoveries (character specific, but very effective), and the FLUDD can pressure people at the ledge who try to do a getup attack by forcing them to fall off. All in all it is one hell of a good attack for ledgeguarding.
When you hit someone with FLUDD, it does not interrupt what they are doing. This makes the FLUDD very good for spacing and therefore punishing an opponent's spacing mistakes since the FLUDD itself has almost no ending lag.
Also if you see Ness or Lucas in a crouching position, FLUDD will kill them. =P
Falcon kick is good for...approaching. Not that it's bad, but it's just okay.
Lastly I'd root for Mario any day. How can you not love an Italian Plumber voiced by Charles Martinet? =(