If you buy into multiverse/parallel timeline theories, both can be the Batmen of the Future. Both can officially take over the title, but neither one has to a permanent fixture. Besides, other people have taken over the Batman mantle in future timelines, including Dick Grayson, Tim Drake, Damian Wayne and Bruce Wayne Jr.
Batman Beyond seems to be set further in the future than Future State. In Future State, everybody looks a similar age as they are in main continuity. In Batman Beyond, Bruce is visibly older and has gray hair.
So in this case the answer is both, but at different times.