Given the fact that the Milan-Bologna-Florence-Rome-Naples line is the backbone of Italian train system, trains run much more frequently (and fast) there.
The Pisa-Rome coast line is relatively slower and less well served.
In fact, with current schedules, the best choice (in terms of time - 3 hours) to go from Pisa to Rome would be via Florence, with one train change.
Schedules are easily predictable, since they are the same every hour. For example:
Pisa 08:29 -> Florence 09:33
Florence 09:53 -> Rome 11:30
Just add 1,2,3... hours for the following trains.
The same thing is true in the opposite direction:
Rome 08:30 -> Florence 10:06
Florence 10:27 -> Pisa 11:31
and so on, adding one or more hours.
Of course, these are not the only trains available, but they are the best combination in terms of speed and convenience.
Have fun.