This is not a holy war because nobody likes trackballs (except me) and they are very unpopular, but anyway I think trackball is better. The one I have is Logitech® Cordless TrackMan® Wheel, previously owned the same thing but wired, not cordless, for 2 years. I am talking about thumb-driven trackball, as I do not understand how can anyone use a trackball that needs several fingers or hands just to rotate the ball - in everyday life.

Why is this ugly piece of plastics better than a mouse (for me) - simple, it has too many advantages against mice:

1. It’s stationary - you don’t have to move it. Your arms rest (only your fingers move), absolutely health-friendly
2. It’s stationary - you don’t need place for it, you can work everywhere, no problems with surfaces - I can even work on my leg - not talking about laptop
3. It is more reliable as you do not have to move it. Unlike fragile mouse, this is like a solid rock

It is same precise as a mouse, can be cordless too.
The only disadvantage for me is that you have to work with clean washed hands only, otherwise you have to clean it twice a day - anyway cleaning is very easy and takes 10 secs only, maybe it is not a drawback at all

About usability and ability to actually use it comfortly for everyday life as a replacement over a mouse - yes it is possible. You have to get used to it, and this period takes around 2 months after you can act same quickly as with a mouse.. But I think worth it.