The background is very cool looking, but it is not as cool as landing a knee on your opponent, so I watch the fight.
Anyway, I don't think this stage is amazing for Falcon, but it certainly has some aspects of it that help him. The tilting doesn't **** over Falcon as much as others, I believe I've mentioned. Some characters it can **** over though: Bowser, Ganon, Ike, PT, Peach, Mario, Link (he'll probably tether), Marth, ZELDA, Snake, Wolf, Olimar (methinks).
I might be wrong on some of these and maybe I've left some out. The point is, look for who you screw on recovery. Don't take everyone here. Leave Battlefield for that. The three platforms are nice for Falcon, but they're nicer for other people. Taller people. DK, Bowser, Ike, Snake, Wolf does nicely here. Still, they're good for tech chasing. The tilting can also mess up various projectiles, (I'm thinking the Earthbound kids PK fire stuff,) so that's always good.