As plowboy said, pressure and flow are key points.  I know some in this area have burnt up the pump for a dump trailer when using them for a belt trailer; I have a 3" wide gear pump that was given to me as junk because it no longer will run a belt trailer.  The Trinity belt trailers here usually have rather small hydraulic lines and will not handle the flow of the larger pumps.  Combine that with the fact that the relief valve must be set for a higher operating pressure, the pump over heats.  Some dump trailers apparently will use a pump with 45 gpm flow and higher.

I don't recall the minimum flow requirement for my Trinity trailer (I believe it is in the 12-16 gpm range) but it will operate using my Permco P3000 series pump with 2" wide gears and a maximum pressure of 2000 psi.  I see that some of the Aulick belt trailers call for a minimum of 20 gpm at 3000 psi.

Permco makes a pump which has an air operated relief valve so that you can increase the pressure setting from the cab when you switch to the belt trailer.  That pump will pump 37 gpm at 1800 rpm at the pump. 

The operator is probably also an important consideration.  I can bump my engine speed up to about 1000 rpm if I'm unloading where I can unload fast; I often speed the engine up to clear the belt at the end of the load.  If I had a higher capacity pump, that would not be needed or advised.

Unless you are using the trailer as a metering box, unload time is usually less than 10 minutes and then there is time to allow for some cooling of the oil before you need to run the belt again.

I hope this is helpful.