Basically there is no difference between hydraulic and hydrostatic motors. The one version controls its speed through speeding up or lowering the rpm of the pump, while hydrostatic keeps the pump going to maintain the same working pressure, and a valve regulates the speed and direction.

Advantages:
- Even at 1 rpm you get maximum torque
- very precise motor control

Disadvantages:
- You need more parts, so it is heavier than just a pump and motor.
- 1 bubble of air and the system either doesnt work or with way less power, even chance of damage.
- Chance of leakage is big. one leak, no pressure, no drive.
- you need to keep the pump going at all times to keep pressure up, so it takes more battery power.