As a trackball heavy user (i use both thumb and index ones, with both hands) I avoid playing FPS without a mouse!

the thumbs trackball is more precise. But still not good. A good and cheap microsoft mouse is always with me when i'm playing FPSs.

Also, even if the control wasn't an issue, no trackball has more than 300DPI. EVER. The minimum for mouses is 400. I don't know why that is. But even the overly expensive Kensington ones are crappy even to click on a 10x10 button on regular usage, let alone to headshot in a FPS.