I have had experience with the Mazak laser, also with a Mitsubishi. Our first laser was a 1500 watt Mazak, which would cup up to about 1/2" mild steel. This was a 1996 model, I believe. A few years later we wanted a laser with more capacity, so we bought a 3000 watt Mitsubishi. We were very disapointed with the Mitz. It was constantly down for maintenance issues, and would only cut up to about 3/4" and that had a poor quality edge most of the time.
I think the biggest issue was the design differences between the two machines. The Mazak was made with a bed that moved in the "x" direction and the head moved in the "y" direction. The x direction being the 4' on a 4' x 8' sheet of steel. The laser column pivoted in the back of the machine so the laser path length was pretty much constant. The Mitz design was a gantry machine where the laser head moved in both the x and y direction above the sheet of metal. This required a lot longer beam path, which was constantly changing the length of the beam from the resonator. Theoretically, it should not matter because the beam is not focused until it reaches the head, but it always seemed like there were a lot more mirrors to align and keep clean. Also, the cost of the optics and PMs seemed like they were cheaper with Mazak. At the time, I know Trumpf was a pretty good laser too, not sure how they compare these days though.
What are you cutting on the laser? Keep in mind surface quality of the raw material is very important! At the time, we could get a grade of steel sheet that was "laser" grade, that was processed differently than standard sheet metal, so it would not have as many oxides on the surface.