Keep the bearing race puller IN LINE WITH THE STEM NECK! If you're not careful and overly enthusiastic (especially with a slide hammer type puller), you'll wind up 'egging' the neck out or jamming the race into the sides of the steering neck.
If you're going to 'tap' them out from the opposite side, small taps in a circular pattern, over and over again work best to avoid the aforementioned pitfalls. Usually if you get one out, the use of a socket of appropriately close tolerances can act as a driver to remove the other one without the tap-around-in-circles routine.
As always, YMMV...
