I just wanted to drop my two cents:
The MU is more than likely either 55-45 for Falcon, or dead even. This is due to the fact that both of these characters have above average mobility, have near if not completely guaranteed follow ups off of throws, and tilts on each other. and they can both either gimp, or send each other so far off stage that it results in a stock, or they're just plain sent to the blast zone.
Now, as far as ive been able to observe of the regular Falcon main that places like 4th or better in PM tourneys out here, when he deals with Ike, it is definitely a grab, and dash dance based MU. Ike is still a Fire Emblem character, so you have to respect the reach he has, but this also means that he is subject to the mid percent up throw to knee combos. all of his aerials except back are are exceptionally slow or mid speed start ups, so falcon typically shouldn't have much opposition when following up after a grab.
Now keep in mind, even though its a pretty grab based MU, that doesn't mean you can stand still. Ike can rush in with quickdraw jump cancel shenanigans, and go to work as fast as you can. You have to be patient and respect his reach in the neutral, and also be aware of his 3 string jabs. it hits a lot harder than average, and can put you in really bad situations. That's not even mentioning his grab and tech chase game on fast fallers. you just want to be aware of when ike is either on the ground, short hopping, and also familiarizing with your opponents quick draw habits. if he is on the ground dash dancing, he'll have to commit to either waiting to CC a nair approach you are doing, stop the DD and wait in shield, or he may just flatout try to get away from you, and dash back in to punish you.
Also, don't try to sit on the ledge when he is recovering. if you are going to intercept or attempt a gimp, do it while he is charging quick draw, or try to intercept him before he hops off the wall. because there is no real way to gimp ike with falcon after he activates his up-b. so its really a combo to death kind of MU, which is relatively easy with falcon if you are comfortable with landing follow ups to knee, bair, or even an up air if you are off stage.