Mr. Roadkill95:
Most of the debate seems to be coming from folks that own BX series tractors.
As a BX owner, please let me clarify the issue: The HST on the BX does an exceptional job of "braking" the tractor when the engine is running and providing pressure into the HST. Personally, I use the treadle to perform 100% of my acceleration and "braking" maneuvers, even on significant slopes (when they get too steep, just be sure you're in Low Range...).
I use quotes around "braking" since it is simply directing hydraulic pressure to respond to the treadle, and this includes slowing down and stopping the tractor when the treadle is moved to the neutral position. At no time does the treadle engage any type of dedicated braking mechanism...it simply controls a very responsive HST. When my Backhoe is off (less weight on the rear tires), my HST will actually lock up my rear wheels if I direct it to do so.
This is important because when you turn the tractor engine off, the machine is free to roll in whatever direction gravity directs. If you are on a slope, it WILL roll freely unless you have the implements on the ground or the parking brake firmly engaged.
That said, the parking brake on the BX series STINKS. At least mine does. It does only a marginal job of holding on a slope. I have personally NEVER used the parking brake to actually slow me down...the treadle/HST does an exceptional job of that. I use it as I would a hand-brake in a car...nice when you're parking and there if in a dire emergency while in motion. It has never bothered me that it is on the same side as the HST treadle as it is only used when your foot is NOT on the HST treadle.
SOOOO, in response to your original question, BX owners would normally use exclusively the HST treadle to control all movement on a hill UNTIL the tractor is going to be turned off. Then you would have to make sure the parking brake is firmly engaged AND an implement is placed on terra-firma. Otherwise, she'd roll down the hill.
Not that it's happened to me or anything silly like that...
And everything I said may be more untrue for other Kubota tractors, but I can't speak to that. I just wanted to clarify the debate that seems to be brewing.