I currently use the RCBS Universal hand primer, it has a square tray and uses no shell holder. It works fine but sometimes does not hold a case very well. A case will pop out or a series of cases just won't be gripped by the shell holder jaws. For instances, brass 410 shot shell hulls do not work in the RCBS Universal.
I also use, on occasions, the RCBS Universal APS strip hand primer.
I still prefer the old, discontinued Lee Auto-Prime but since I cannot get replacement parts for them any more, I am saving mine for instances where the RCBS primer does not peform, like the brass 410 shot shell cases.
I have one of the new Lee Auto-Prime XRs. It works ok and the primer feed works better than the old Auto-Prime or the RCBS square tray. I have kind of gotten used to not fooling with a shell holder, so the Lee is another back up.
I find round trays work better at flipping primers. There are no corners for the primers to get "stuck" in. But, not a big deal either way.