There's a reason Bloodborne is a PlayStation 4 exclusive. And even though that reason is probably because Sony paid a crap ton of money to have it on its new console, that's not the reason the game's director is giving us.
According to director Hidetaka Miyazaki of From Software, Bloodborne just isn't possible on any other system; although, his response is likely referring to why it's not coming to PS3, not why it won't be available on Xbox platforms. We already know the answer to the latter question. Regardless, here's what he told PlayStation Lifestyle when asked why the action RPG is only coming to PS4.
I always wanted to make a game set in the Victorian era, but to make it look good — with all the clothing and the architecture and things — required a console more powerful than the ones that were around. the arrival of the PS4 finally gave us that. Bloodborne isn’t a game that could have been cross-generation, it was only possible on PS4.