Between the one pictured above that I just bought and the one with the handle which do you like better and why?
Since you have all three you probably use all three but how do you determine which one you are going to use? Does it depend on the type of pizza you make? I do like that rocker knife but my wheel works pretty good but later I'll get the rocker. Thanks.
Ok, lets see. The palm cutter is the one I use the least. For some reason it's not very comfortable in my hand. My daughter gave it to me as a gift, so I keep it around. Usually, I leave it on the table for guests to use as needed. The handled cutter, I use most just because I've had it the longest and it has a larger wheel than the palm cutter which helps with the dragging issue. Also, having limited space on my counter, it's easier to use than the rocker. The rocker, however, is tops when dragging the toppings is an issue, but you need room to maneuver the thing, which is why I'll use it primarily on a large flat cutting board on a table outside by the wfo. Also, I believe the rocker is built for speed, but to be honest, I'm not very fast. If I tried to be, I'd probably cut my finger off or something.

Mostly, I bought the rocker because that's what we use at Norma427s' market stand. It is kind of pricey though.
For general use, I'd recommend a handled cutter with the largest wheel you can find. If you look around you find ones with replaceable wheels in case they get too worn.