In terms of punish game, Falcon can punish himself really hard and it's generally pretty straight forward. Same with his edgeguarding. Assuming you can tech chase falcon and edgeguard him, the important step is getting that opening that allows you to do so.
Contrary to what most people in here are saying, just spamming nair isn't going to net you the win. The Falcon ditto is a matchup that I'm not comfortable in, and as such I've been studying it a bit lately. If you watch a falcon ditto you're seeing lots of dashdancing. They're doing it to bait an approach from one another. If you just mindlessly throw a nair where they are, then you are doing just what the person wants. A typical punish to a badly spaced nair is a grab. And getting grabbed in this matchup should lead to a lot of damage.
Now I'm not saying that nair is a bad option, it's falcons best approach, but that doesn't make it any less predictable and punishable if they're expecting it. So now you have to mindgame the opponent and to making your nair viable. There's plenty of ways to do this, such as getting a read on your opponents dashdancing, and overthrowing your nair hitbox onto where they will be by the time you approach. Another way that I enjoy is throwing a nair out that looks badly spaced and punishable, when it is actually safe. That usually will make your opponent attempt to punish you, and you can react and punish whatever they do instead.
I can see this thread is a bit old but I felt like giving my two cents because writing stuff out like this helps flesh out my thoughts, hope you owned the other falcon and styled hard. Also make sure to check the falcon index about the Falcon MU, it's got some good stuff in there.