As with any input device, personal preference should rule choice. That said, relative to mice, trackballs have the following advantages:
A trackball remains in place, and so requires less free desk space than a mouse.
The trackball roller ball contacts your thumb rather than the desktop or mouse pad, which means it is less likely to require frequent cleaning. (However, "red-eye" optical mice do not require cleaning and so eliminate this advantage.)
A trackball is often the better choice for 3D gaming and similar programs, where pointing and clicking are the most important functions.
Some evidence suggests that using a trackball is less likely to cause RSI than using a mouse.
Trackballs have the following disadvantages:
Most trackballs are designed such that you guide the pointer with your thumb, which is the least dexterous digit. Accordingly, many users find it harder to position the cursor exactly with a trackball than with a mouse.
Most people find a trackball clumsier than a mouse for operations that depend heavily on click-and-drag, such as creating and editing documents.
Some evidence suggests that using a trackball is more likely to cause RSI than using a mouse. (Yes, we know...)
Mice and trackballs are inexpensive enough that you should try both if you spend much time at a computer. If you have never used a trackball, doing so requires some adjustment. Many people find Microsoft optical trackballs?which look like a mouse with the red optical dome on the top or the side, depending on model?to be the easiest trackballs to adjust to.