The punish game for spacies vs Falcon is pretty one-sided on FD, IMO. But in theory, if you can tech chase spacies well, it's just as bad and they'll be scared to take you there. It's just a lot more work techchasing then getting one grab or shine by Fox/Falco leading into a huge punish.
Best Stage for Falcon is a grey area, as it seems that almost every Falcon has a different opinion on what they're favorite stage is. I would say that it's more based on yourself and how you play. Naturally, larger stages are better suited for falcons mobility, but we've seen that FoD can be a technical playground if you're quick enough with your fingers. That said, I rarely stage strike to FoD, and I exclusively CP to Battlefield or PS. Those are my two favorite stages hands down.
I think Falcon has a disadvantage in stage striking against Falco and Fox. If the Fox is grimy, they're gonna ban Battlefield and Dreamland and leave you with Yoshis, FoD, and FD. I personally go to Yoshi's, and ban FoD and FD. I've seen Darkrain strike to FoD first game, which win or lose, the opponents next CP can't be any worse because you can ban their next best stage. This makes their Game 3 (or 2) counterpick much less volatile. I use this strategy often, excluding doing it against Falco Fox and Sheik. I think against those characters, it's best to try and strike to something else.
Anyways I kinda blabbered a bit. tl;dr falcons best stage is your personal favorite! The stereotype is that FoD and Yoshi's will stifle Falcons movement a lot and so a very general rule of thumb is to avoid them. Often in stage striking you have to pick between the lesser of two evils.
