For 1000 euros I would favour the TV simply because 1000 projectors tend to project vibrating images that will give you a headache.
You'll also want to consider the room dimentions into the equation. you'll have to put the projector at the right angle and the right distance to have a clear image. Also, it'll be more job to pass the wires from the top to your PC. Good projectors usually go from 4000-10000$( look here if you don't believe me : http://reviews.cnet.com/1770-5_7-0.html?query=best+proj...) , so a 1000$ projector.... I wouldn't dare to buy one at that price, especially for gaming.
Bottom line is : Don't buy a projector or TV for gaming, buy yourself a great monitor... one that can support good resolutions. The best thing for 1000$ is a 30" monitor here, they usually cost 700-1000 euros (Hp ZR30W, HP lp3065, Dell U2711 [27"], Dell U3011) or you can go with a 3D 27" from samsung S27A350 or something like that.
My motto here would be : bigger is not necessarily better, better is better ^_^!