In THEORY an Hydro tractor should be mechanically simpler, therefore more reliable and less expensive to make than a gear unit. All the parts are the same, except the clutch, gearbox and shift mechanisim is replaced by a hydraulic moter and control. In PRACTICE, people have been making gearboxes for a long time, they are well worked out.
I'm sure the higher price of a hydro is based on demand, not on cost to the manufacturer!
If all you are going to use the CUT for is FEL work, then hydro is what you want. On the other hand if all you are doing is loader work, maybe a CUT, which is a general purpose machine, is not what you need!
For all around use, I find a shuttle works best for me. There are some characteristics of the hydro, at least as implemented, that I don't like, and I find I am not equipped with enough right feet to operate the controls (I brake-steer a lot)! For me, a synchro shutle would be perfect (mine is manual).
In the end, there is no reason that the inherent reliability should be much different. If there are differences, it will probably be due more to weaknesses in a particular design or to the operator.