Actually the difference in performance is quite a bit, mostly in your GPU Vram. But it also depends in the game. Nowadays the sweet spot for 1080P is a good card with 2GB ram, like gtx 760 or better, and r9 270 or better. When it comes to 720P a gtx 750 is enough.
It also affects the cpu if you have a low end one.
Well, the difference is 2,0736 million pixels for 1080p that need processing compared to 0,9216 million pixels for 720p. But fps wise, it is not directly comparable. Maybe 20-30 % difference? I don't really know.
Actually the difference in performance is quite a bit, mostly in your GPU Vram. But it also depends in the game. Nowadays the sweet spot for 1080P is a good card with 2GB ram, like gtx 760 or better, and r9 270 or better. When it comes to 720P a gtx 750 is enough.
It also affects the cpu if you have a low end one.