There's a reason why both types are still available.
It all depends on what type of work you'll be doing MOST of the time... or if you just desire the added flexibility of a hydro.
If your work is fairly linear, focusing more on efficiency and consistent ground speed than anything else... you will likely find a gear/shuttle tranny to be more efficient and beneficial. (Example: row cropping, etc.)
If your work requires fluctuating ground speeds, intermittent engagement, or frequent changes in direction... a hydro will make things MUCH easier. (Example: loader work, grade work, mowing in tight areas or around obstacles, or working on hilly terrain, etc.)
As I said before, it's what you do MOST with your tractor. Hydrostatic transmissions require a little bit more maintenance and are generally a little bit less efficient in terms of drivetrain efficiency (85-90% for hydro, compared to roughly 88-92% for shuttle). The slight loss of true efficiency will more than make up for itself in productivity gains, if your application is suitable. The only added maintenance is fluid/filter changes. It is possible to overheat a hydro tranny in some heavy duty applications, but most manufacturers have alleviated the problem in newer equipment. Extremely slow operation for long periods of time can result in overheating the fluid. If you're doing meticulous work, just remember to move the tractor enough to cycle the pump fluid every few minutes (again, most manufacturers have alleviated this problem in newer equipment... so unless you're buying used, it's a non-issue).
For my personal applications, I always choose hydro, due to the hilly terrain of my property. Most of my usage is loader work, mowing, and property maintenance... so a hydro is a huge time saver, as it allows me to keep both hands engaged with the wheel and master cylinder controls.
I do have a Kubota with a gear tranny. When I need that extra torque at low speed, it's my go-to... but honestly, I'd do better with a slightly higher horsepower hydro and a three or four range final, as the only thing I use it for is "cut work" (grade work that involved cutting ground, instead of simply mowing aggregate or loose soil).
I hope this helps.