Anyone can feel free to correct me on any of these because I'm just writing on my experiences and studying of the Captain.
Falcon's speed is going to be a big thing to contend with, especially that sliding grab. Add to that the raw hitting power and combo capability, and it's a dangerous situation.
A common combo you'll see from them is grab, down throw, Uair (maybe twice), then maybe attempt to spike with Dair (depending on your damage and location). This one will hurt. FF-Nair is one of your better defenses if you can DI a little away midair.
Intelligent projectiles are your friend.
If a Captain Falcon is closing the gap, you need to be very sure you have enough space and time to throw that boomerang. The windup on it is just long enough that the Captain can hit you before you throw it. You'll get punished if you keep spamming it and get predictable.
If you're in the air and he's having to close to you from the ground, angle your boomerang, FF Nair, or Zair. Seriously, Zair is your friend. Use it.
If he's trying to dash and grab you, start grabbing him first and punish him. If you become predictable, you'll be in trouble.
Be very ready for bombs and arrows to break his momentum. Boomerang works fine, but remember if he's too close, he'll interrupt it and punish you.
In the air, your Fair works well since it reaches further out, but keep this one fresh.
If you can Sidestep and Dsmash, Dtilt, or Ftlit, you can punish them.
Use quick attacks. I've found that if you're on the ground and he's in the air, we can pepper him with attacks fairly well. Angled boomerang, Bomb spam, Utilt, Usmash, SH/FF Uair, Nair, Bair, Air Dodge to Dair (risky, be very careful on this, it will hurt if you mess up! I suggest only using it once - maybe twice if you MUST). However, this can all go out the window if he decides to Falcon Kick into the ground, at which point shield and counter.
For those Captain Falcons that love to spam Falcon Kicks and Raptor Dives, shield and counter. You can try to grab or bomb to break this up. You have to be precise though, or else it'll hurt. The good news is that the lag after the falcon kicks and raptor dives works well for us.
Every so often, I see one who tries to reverse falcon punch to edgeguard - just don't fall into this. This is really uncommon, but be wary. Remember, a Falcon Punch can be deceptively quick, and now that it can turn directions, you have to decide to either punish immediately or make sure you're far enough away to not be touched. If you're indecisive, just give it space and punish him AFTERWARDS.
Falcon defending the ledge in the air is deadly - especially his quick spiking Dair. The guy hurts when we're trying to recover. Tether recovery can help but remember, we can still be spiked or hit while we're tethering to the stage. But don't be afraid (if you have the angles) to boomerang, bomb, or arrow. If he's waiting for us while we're on the ledge, don't just jump, roll, or attack in the most standard fashion (we'll get grabbed, elbowed, or knee-of-doomed pretty hard). Sometimes, short hop and lead into Fair or Nair or Zair. If you have a bomb, use it.
A smart Captain Falcon will mix up his approaches, because he wants to plant his foot firmly between your lungs and lower intestine. What I mean is, his speed and agility allow him to quickly approach, quickly stop, jump, or quickly swap directions to wait for your ranged attacks to finish. Sometimes just switching up your timing on your projectiles is enough to help here.
In the end, there's no magic formula that constantly works. We have to utilize all our weapons, play very smart, very tactical, and realize that we can't make many mistakes or be too predictable. We especially can't be predictable here. CF is fast enough and hits hard enough that, should we be predictable, we will be in serious trouble because of the amount of punishment we'll take.
