I think it's far too soon to be projecting or making predictions about how this will turn out. It sounds like all they have at present is a basic idea: putting the two characters together.
While certainly not perfect overall I quite liked the recent Nolan Batman trilogy. I went into MoS with a mixture of hope and trepidation because of different things I'd read and heard, but in the end I thought it was pretty decent. It certainly wasn't perfect and there are a few little things I'd liked to have seen as well as a few things I wish they'd done differently. In the end my biggest gripe is with the final action scene: totally redundant and overdone. But the rest of it I can live with.
Regarding this announced project, I'll wait and see. I think it's reasonably certain it will be a Bruce Wayne Batman and not anyone else. I think it's likely he'll be a more than cameo like character in the story. It's simply what most people will expect and line up for.
While they might indeed reboot Batman for this---and thereby open the door for further solo Batman features---I certainly wouldn't mind seeing Christian Bale come back for this one more story (assuming they decide to keep it all the same continuity). Bale did say he was done with the character, but I'm pretty sure he also said that if Chris Nolan were involved and it was a good story then he'd be up for it. We'll see. That said I'm not keen on seeing a Joseph Gordon-Levitt as Batman simply because he's not Bruce Wayne (in that continuity) and he just doesn't have the right look to him (in my eyes).
It could work in the same continuity as the Nolan trilogy simply because fantastical elements were introduced into that continuity and the events of MoS can be seen as happened sometime after TDKR. Bruce Wayne could see the appearance of Superman as a potential threat and be convinced that he's the one who has to look into it. In the beginning it could indeed be versus each other, but then come together to combat a larger threat. Saying that it could be loosely based on Frank Miller's work might only be a way of conveying the general story idea they're considering without adapting the exact original story point-for-point.
For now I'm cautiously hopeful for this even knowing that it likely won't be everything I think it should be and will likely do some things I'd wish they would do differently. Pretty much like MoS and the Nolan trilogy.