I have the RCBS and Forster versions of the press mounted sets. They both work very well, as long as there is enough of the shank for the collets to get a grip on.
That's why I have a Kinetic puller as well.
The nice thing about the kinetic puller is that it doesn't do any more damage to the bullet than was done during the loading process.
I've never had an issue with collet pullers, other than some Milspec ammunition with heavily crimped necks and pullets seated to the ogive.
Ganderite sent me a neat little press mounted puller which is caliber specific, it's no longer being made, so I won't go into detail. It has spring steel petals, which the bullet is pushed through and as the ram recedes, the petals grip the bullets, even on the ogive. However, it does leave marks on the bullet, which don't seem to effect accuracy.
OP, if you're pulling bullets from handloads, unless you crimp the necks, a kinetic puller will usually do everything you need to do, if you use it properly.
Some folks just can't bring themselves to apply enough force to the unit to get the job done, or they use it on surfaces that are soft or absorb the impact. I use a two kilo, lead bar as an impact base.