I've owned both, and think they do the same work but differently. Maybe it will help if I describe going about the common job of using the FEL to move a pile of dirt.
First thing to know is that most compact tractors with power shift has a manual clutch, it's just that it is automaticsally clutched when you shift through forward gears (but usually not when you shift ranges). And Power Shuttles don't all have the same sort of clutch. Some have a regular foot clutch in addition to the power shift, although most will also have the automatic clutch that is triggered by either the shifting motion or by finger pressure on the power shifting lever.
Some power shifts - particularly larger tractors - do not have the same automatic manual clutch as compact tractors, but instead they have a torque converter. Torque converters cost horsepower. so those power shifts are usually found on tractors over roughly 65 hp and on up.
With our JD and Yanmar power shuttles I would either choose a very low gear or use the clutch at least for the difficult part of each bucket fill. If the pile was at all tough, I'd use the clutch several times as I inched into the pile. When the bucket is full enough, some power shuttles require you to use the clutch when you shift into reverse to back away from the pile as you are lifting the bucket load ....and some do not need any special operator clutching for reverse because they automatically clutch when you make that shift from forward to reverse - just like they automatically clutch for you when shifting going forward.
By "Hydro" I think you mean a Hydrostatic Transmission - a HST. With the HST transmission very few tractors have any sort of a clutch....a few do, mostly as a safety for starting the engine, but it's rare.
Mine does, but even so, I don't use the clutch our HST except for startup, never touch it after that. The foot pedal that controls the HST automatically changes the internal gearing and the throttle to give the maximum drive force for that the pedal position. As I approach the pile of dirt and drive into it all the changes in speed and torque are done by the tractor in response to slight movements of the foot pedal.
I much prefer the HST for loader work. It is effortless.
But power shift works just fine, a few more motions perhaps, but it becomes instinctive.
Power shift is often less expensive than HST - and he Power Shift does have an efficiency advantage. Slightly more engine horse power goes to the tires with power shift than with HST. So it is more economical of fuel and power.
I really liked our old power shift with the fingertip clutch....but after getting a HST, it is even easier to use for FEL work and for any type of quick chore work or lawn mowing. For mowing a big field or plowing or any tillage work...or for towing a trailer up and down a lot of hills, the powershift might get the nod. At least from me.
Hope this helps,
rScotty