As far as I know, there are three types of separator (my descriptions are my own, not the technically correct ones):
1. the wedged fork, designed to be whacked in with a hammer
2. the simple press tool, that uses a screw acting directly on the stud of the ball-joint, to push it out
3. the side lever type, which has a fulcrum to provide mechanical advantage to push the joint apart
Unfortunately, I don't have enough experience to tell you which is best. My guess is that 1. might be crude but effective, provided you have room to swing a heavy hammer (I have a fork tool, but have never actually used it); 2. (the type I use) is compact and will work OK so long as the joint isn't very badly stuck; 3. I guess must apply more force but is more expensive and needs enough clearance to allow you to deploy it.
Perhaps someone who has a better idea of which to use could add some advice.