First of course paint your room.
Okay, I think the question is which will do a better job of handling ambient light/secondary reflections? All things being equal I have to say more horsepower to overcome the ambient light rather than pretend you can solve this problem by finessing it with a gray screen.
High Power especially for your setup if your eyes are anywhere near the light path. If you are sitting off axis maybe a gray screen...and a 3000+ lumen projector.