Much of this debate is personal preference. You really need to try both to see which suits you best for the work you do.
I bought and enjoyed a shuttle shift 38hp tractor 19 yrs ago, but I'm 78 and thinking I'd like to end my days with a new tractor. Most now seem to be hydrostatic. I just talked with my brother-in-law who has both transmissions and he recommended staying with shuttle shift. I do some mowing and he says his hydrostatic gets way too hot when mowing. He likes it when doing dirt work and moving hay, etc. but not for something where you'll be driving it steady for a long time. It seems the dealers around here are mostly pushing hydrostatic. What's your experience?
I'm a little older, and I also grew up with geared tractors and then powershift/shuttleshifts.
When we went looking for a new tractor in 2008, I was worried that the HST wouldn't stand up, but they do. Yes, I've heard they can get hot at full throttle and full load....but so does any tractor. I resolved to keep the cooler clean and to look for a HST that had more ranges so as to match the tractor to the work. In that respect, a HST is no different from any other transmission.
Our 60 hp Kubota has three ranges and Hi/Lo in each, so 6 speeds forward and in reverse.
The HST shines when doing careful close chores or any loader work.
The big difference is something I didn't expect, it's that the hydrostat makes me look forward to using the tractor because it is just that much easier on my old body. Much more relaxing to run.
Tell your brother I worried about the heat too. And like he says, I always leaned towards the shuttle shifters myself. But the model tractor we were wanting only came with the HST+ tranny.
So what I did after I bought it was put an inexpensive temperature gauge on the lines to and from the hydraulic radiator. Here's some photos. I don't mow with it, but hard backhoe and loader work doesn't change the temperature much at all.
rScotty