I can run the game smoothly at 60 FPS (including explosions etc) at 1080p, with 2x SSAA and 2048x2048 shadows. Higher than that, and my GPU struggles (HD6850). I don't have one of the new consoles, but it's light years ahead of the X360 version. As reports say, the game is quite CPU bound, so a weak CPU is a bigger problem than a weak GPU. Glad I have an FX-8350.
I have an issue with my Xbox One controller. This is not exclusive to DOA. Assassin's Creed I and II also had this issue with my Xbox One controller. The triggers don't register.