Epic Games' CEO Tim Sweeney recently indicated that the "Samaritan" tech demo would require 2.5 terraflops worth of processing power to run, according to Develop. For reference, that's ten times as powerful as the Xbox 360, which can manage .25 terraflops.
The "Samaritan" demo was built to demonstrate what might be possible using the next generation of the Unreal Engine, though it was running using the Unreal Engine 3. Unreal Engine 4 is expected to release in 2014, with more details from Epic about the middleware likely at GDC 2012.
A recent rumor implied that Microsoft will not be emphasizing raw processing power as much for the next generation of Xbox as they are features, like a touchscreen controller.

