The reason they don't fit together is not "one is dark the other one is bright". That's fine and desirable when it comes to the Superman-Batman dynamic. In fact I'm actively hoping that despite the fantastical nature of the DCU Batman he'll keep the darkness that's made him so compelling in the modern era of comics.
The reason they don't fit is because Pattinson's world is very decidedly NOT a world in which heroes exist and have existed for a long time. It is not a world with sci-fi technology like the ones that Mr. Terrific has, it is not a world where stuff like the Creature Commandos exists, and Pattinson's Batman is very very very much not designed to be up against the threats that a world like that has to offer, he's designed to be an urban crime fighter that'd be a big deal in a realistic world like our own and making the transition from that to one that can stand toe to toe with Mr. Terrific, Hawkgirl, Metamorpho, Green Lantern, let alone Superman would be very very very hard and kinda destroy the whole character in the process.