Has anyone ever thought that maybe Sora and BHK don't have that much in common? As of now, the only connection between BHK and Sora is that Namine placed the memory of Twilight Town, BHK's home, into the other side of Sora's heart, and that's how he was able to access it.
The way I see it is that there are four different worlds:
Sora's World
Darkness World
Light World
The world in-between.
I think that Sora fights enemies from the Darkness World and BHK fights enemies from the Light World. That's pretty much the only reasonable theory I can come up with. It's just that the worlds entertwined when Vexen brought Sora to Twilight Town, and everything screwed itself up.
Edit: On topic -- I think that if it was possible for the story to flip back and forth between Sora and BHK, it would progress through the same story. It wouldn't be like KH: CoM where you did Sora's story first and then Riku's. However, I doubt that BHK will be a playable character. That would be sort of like making Riku a playable character in the first Kingdom Hearts game.