I have a Hornady trimmer that looks identical to that. Bought it around 1990, I would guess. I use Lee shell holders in it without issue. I find the hand crank a pain, and if you are doing more than a handful you will probably want to mount a drill onto the cutter shaft. That's easier said than done, as you have to mount the drill so that it is supported, perfectly aligned with the shaft, and capable of sliding back and forth. It takes some thought to figure out how arrange that.
It works well enough, but I find I usually end up using the Lee trimmer mounted in a drill most of the time. The Lee is faster to set up, no depth adjustments required, more portable, and faster to get cases in and out. It's hard to think of a catagory where the Hornady offers any real advantage.