I use the press mounted primer on my Co-Ax press. A few years ago, I had a competition on a Sunday afternoon. I shot some practice rounds on Saturday. So Saturday night, I was loading my competition rounds when my RCBS hand primer failed. I was priming the .338LM case. I had called RCBS customer service the week previous to see if ths hand unit would do the magnum case. I was told that, yes it would. With no problem.
On the 5th or so case...snap. The pivot rounded smooth because of the extra force needed for the bigger case. Most likely because it was cast from very soft pot metal. I was in a pickle. I needed to load these cases for Sunday's match. I had never tried the press primer on my Co-Ax. So I decided to try it.
I was pleasantly surprised by the ease of the system. That large handle generates so much force, but It is also very tactile. Meaning that you can feel the condition of the primer pocket...loose, or firm, or tight. And seating was extremely positive. Meaning that you can really feel when the primer is fully seated. Something that escapes you when using a hand unit.
I was so happy that I haven't looked back since. My Co-Ax's press mounted primer is all I use. From .44mag, to .223rem, right up to the .338LM case. Now you can make up your own mind, but for me, the versatility of this system and the ease of use... I will never use a hand held unit again. But the big reason is for the "feel" when you seat a primer. Owners of the Co-Ax press will understand. For me loading precision rounds, it's a no brainer.
Ymmv.
EDIT: My apologies to those people who don't own a Co-Ax.