Well, they both have to meet a certain minimum really. My threshold for acceptance on mechanics is a lot lower than it is for aesthetics.
I also still have trouble with accepting the characters existing in the same place at the same time. I understand that there are archetypes for these sorts of things, but stylistically and conceptually, they're just very very different games. Blaz Blue tries so hard to be edgy, and grim while Arcana Heart seems to be in love with its light-hearted "Mahou Shoujo" feel. But again, like we said before, "lol fightan gaem story" so it's not that big of a deal.
That being said, I still don't see how it would work on a mechanical level either. Would you pick grooves? What about those drive buttons? How would you balance the AH characters to compete with BB characters if the BB guys get the arcana as well? Would the AH girls get drives too? Or would their boost cancels act as drive substitutes? Would the BB guys get the boost too? I dunno. It's all over the place really. I'm sure you could FORCE it to work, but I don't think I'd look forward to it or even expect it to do remotely well.
EDIT:
Taokaka might fit into Arcana Heart. That's about the only thing I can really see happening. And Rachel. I guess she fits a sort of Moe archetype, right?