lol I think its funny how all the non Doc mains think the matchup is close to even. Falcon's nair is bad, but its the knee that gives him the edge IMO. That **** has the potential to kill Doc at such low %'s its terrifying.
Edit: in hindsight, the knee ***** everyone, but its especially bad for Doc on the ledge and what not, turns the match aruond really quick. The way I see it, Doc has to work much harder for KO's then the other way around. They both **** one another's recovery, they both combo one another and tech chase one another really well (if Falcon's tech roll wasn't so horrible this matchup would be much worse for Doc), but Falcon really only needs one good read to set up for a Knee, and Knees == super bad for Doc's horrible recovery. This isn't to say that Doc can't keep up, just that he has to be extra cautious when fighting C.Fal for fear of making one mistake and getting punished to death.
Falcon's nair/bair/uair rip through pills, but nair is really the only practical one to approach with while cutting through them. This leads to Doc baiting that and punishing, then Falcon adjusting to that and repeat etc etc.. eh I'm not a big fan of pills in general, and the Falcon's I've faced don't have much of a problem dealing with them.
So yeah, this matchup breaks down into: Falcon DD camping using nairs to stop pills, and looking for one good read to lead into **** which leads to easy edgeguards, while Doc pokes, buildling damage here and there till he gets a grab/gets falcon off stage and then goes ape****. This is based on playing against Scar, hax and the almighty PC Jona.