I have an RCBS inertia puller and an RCBS collet puller, not really crazy about either one, but...... The inertia puller does get a little messy with powder because the bullet is mixed up in with the powder and they have to be separated. As for deforming the bullets with the inertia puller, I read a good tip on the forum about putting a foam earplug in the bottom of the puller before you use it. I've not done it yet but will next time I need to pull a bullet. The collet puller is the one that I will use most if I have a number of bullets to pull. It will remove bullets three times faster than the inertia puller due to the manner of running the bullet up into the collet, tightening the collet around the bullet and then bringing the ram down to separate the casing from the bullet. I have found that the collet puller "will" deform the die if there's too much neck tension on the bullet. When I am working a load I usually will load five rounds of a particular load at a time so as not to have too many cartridges to pull due to excessive pressure. Also I've never really had good luck with pulled bullets, just not the same as new ones.
I'd also add that the inertia puller will pull anything that anyone would want to pull, even elephant's teeth if one needed to. But I have found that the collet puller has a lot of difficulty with crimped casings, it'll work sometimes it will take two or three bites into the collet, where the inertia puller you can just keep hitting the hammer on a hard object, for me that is the anvil part of my bench vise.