[quote=SwordfishKnight]I'm now imagining a mix between ice climbers and Phoenix Wright. Interesting combo.[/quote]
I don't really know about Pheonix Wright's combat abilities, but here's a more specific explanation: 

Basically, they'd be the same character. They share the same SP, HP, etc. Only one of them fight at a time (I guess it'd automatically be Aiko at the start) and to switch between fighting with Aiko or Akari, you'd press the D button or something. Then they'd do a quick switch animation, and bam now you're playing as the other twin. They'd obviously have some different moves, but largely they'd have the same movesets. Aiko would probably have a few stronger moves, while Akari would probably have more reversals and safer moves (i.e long-ranged?). You logically wouldn't be able to hit the inactive twin, but there'd most likely be a few moves where the inactive twin helps (these would obvs be different based on who's the active twin). As for their actual fighting styles, I have no clue. I imagined Aiko being like Adachi minus thee gun, while Akari would be Rise-esque.