It seems to me like if most of the fight is on the ground , Sheik wins. If it is mostly in air, then falcon wins. The number one thing is to not let the CF get a grab off. Falcon is really based off of his grabs, especially against Sheik. A Falcon's goal is to kill with as low of damage as possible, always less than 100. The main way this is done is either a quick grab to uthrow or dthrow to knee. . .pretty much always. So once you get around 60 to 90 damage, you know that they will be looking for grabs. Don't let the empty nairs and dairs fool you, chances are they are going for a grab to knee. Be patient, most Falcon players are very impatient and play with a lot of energy, if you set the speed of the fight with careful needle and grab placement, you will frustrate them so much that they will start throwing empty knees and things like that, then you have them. Be ruthless with edge hogging. Edge hop bairs, dsmash, jumping needles, all of these things have frustrated me many times. I always have trouble with people that DI away too, it messes up my uair combos. Finally, like I said before, if Falcon can't kill Sheik before around 80 damage, it is very, very difficult to ko her then. It is like if she passes 80, then she gets to 150. I guess what I'm saying is the longer the fight goes on, the more it is in Sheik's favor.
I hope this has helped, I have fought a lot of Sheiks in my day. Sheik is beastly.