HST Pro: Ease of use, anyone can operate it. Safer when working around people on the ground, as you have more precise control. Ability to go any speed, infinite control of ground speed independent of throttle setting. Ability to quickly change direction, no clutching, does not wear out your left leg, ideal for loader work., Ability to change speed when tractor is loading down for instance when brush hogging, and cutter is lugging the tractor, just let up on the hydro pedal until the engine can catch up. I would go as far to say more reliable, No clutch to wear out. Others will differ with this, but I see more clutch failures on here than hydrostat failures. Proven technology, over 60 year track record, used extensively in bulldozers and other heavy machinery.
Cons of Hydro: Hydro "eats" power from engine. In other words, there is some loss, that loss equates to heat production. That is why hydro machines have a cooler section in the radiator, like an automatic transmission in a car. Hydro machines "whine", make a unique noise while operating. It seems the smaller machines make more noise than the larger ones. I can't hear mine over the diesel "cackle". Hydro machines have an extra filter to change, so slightly higher maint. costs.
Straight gear machines (crash boxes). very limited speed ranges, You are locked into fixed speed steps. The more gears you have the smaller these steps are, but they are still steps.. In the low gear count machines, you have 2 actual speeds, too fast and too slow
.. Plus side of gear machines is they deliver almost all of the power that goes into the transmission out of the transmission. Downside is they have a clutch. If you know what you are doing a clutch can last a very long time. If you don't know what you are doing, clutches can last a very short time. If you are old, clutches hurt. If you are young, and have good left knee joints, clutches are fine. Hydro shuttle gear machines allow directional changes without clutching, this is a good thing, from a human perspective, but are actually more complicated than pure hydro machines. They work well though. Bottom line if what you do, involves going in straight lines forward, and you want maximum power to the ground,(example plowing/row crop) then get a gear machine, especially if you left leg is in good shape. If what you do is mostly loader/fork/grapple work then you will profit from a hydrostatic machine, especially if your left leg is not in the best of shape. Hydro machines cost about $1000 more to purchase, and are worth about $1000 more when you trade them in. I have owned 2 gear, and 3 hydro machines, and got a lot of good use out of all of them, but it is hydro for me from now on.