Do you want a serious discussion or posts that are making me think that the Ike forums are turning into the Roy forums?
In all seriousness, I think Ike beats Falcon. Falcon's only reliable kill moves are his knee and his smashes. With no hitstun, no one can combo. Falcon's bread-and-butter is gone. His DAir is useless for starting UAir/NAir combos. Raptor Boost hits the opponent too high. While NAir and UAir are still good for "comboing", they only work with sloppy DI and slow reaction time from the opposing player (in this case, Ike). Falcon has no range - the only way he's going to get those combos in is by rushing Ike or camping. Ike can just space and abuse his NAir/FAir and chip away at Falcon's damage until it gets high enough to kill him; BAir, DAir, or FAir offstage will be enough.
The bottom line is to just space and keep Falcon out with jabs and aerials. That's the general strategy with Ike.