Servos suffer from poor resolution. They are normally driven from 0 to 180 degrees in whole degrees. The cheap ones can't even resolve a single degree. So you get something with about 100 steps that aren't very precise.
Stepper motors have very precise steps. The errors are also not cumulative. It can't step to exactly 1.00 units but the first step might be 1.01, The next step might go to 1.98 and when you go 5000 steps (many revolutions) you will be at 5000.01 from your starting point.
You also don't get to control the speed of a servo unless you are giving it small steps. So you should probably use a stepper anyway.
A continuous rotation servo has no feedback for position. It does not store the home position when powered off.