First of all, my use of the Lee auto-prime goes back some time, so this may be old information to others here.
The original auto-prime(from your picture) worked very well for me, but did come with a caveat to NOT USE Federal Primers. Considering that the design left all of primers in the tray very close to the seating stem, if you had a jammed primer that might be set off, the entire tray would go off. Federal Primers were noted as being the most sensitive in this regard. I believe that Lee redesigned this product in the past but not sure how long ago.
The Lee ram prime system doesn't share this problem and does have the benefit of being able to be adjusted to provide a repeatable primer seating depth. I've never used one, but it should be a benefit for the "bench-rest" set.