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.
I wholeheartedly agree that trackballs suck for FPS games, but most pro FPS players advocate keeping the mouse at a fairly low DPI, so that deficiency isn't really the problem.
I have trouble believing that any device that relies on thumb-only input is going to be anywhere near as good as a mouse, but I hope I'm proven wrong.
Trackballs really aren't _that_ terrible for precision in FPS. Not pro level, but heckuva lot better than the joystick control consoles currently use. I found I had a harder time in StarCraft than I did in UT2K4, but both were quite playable.
I used a Logitech Trackman for seven years, and the biggest issue was that the force required to move the ball around wasn't constant; it would vary depending on how gunked up the little rollers inside had gotten. I had to clean mine out every day to keep it smooth.
If a person prefers using a trackball, that's great, but when the same tools used by the pros costs about $50, there isn't really any other reason to use anything else.