Thermostatic Controls
The temperature is pre-set and the valve will return to the pre-set temperature again when the water is turned back on. The temperature is calibrated so you have precise temperature control. You can visually set the temperature with the calibrated temperature dial.
Thermostatic valves usually have two controllers. One knob/lever to set the volume flow. Another to control temperature. The two controls allow you to have a trickle flow of water through 100% full flow of water at any temperature, from cold to hot. You can leave the temp setting in the same place for years at a time and simply use the volume control to turn the water flow on and off.
A thermostatic valve self-regulates to maintain the temperature where you set it. Changes in water pressure from flushing toilets or other faucets running, will not cause the temperature to fluctuate, like it will with a pressure balance valve. 
The scald setting on a thermostatic valve actually limits the actual water temperature to a specific temperature. A thermostatic valve senses and controls the actual water temperature.
On Aquassure’s Active Living Slide-in Bathtubs, the Safety Plus Thermostatic Fixtures have a deck mount temperature control that you can see and it also has a stop point at 37 degrees to prevent the bather from accidental scalding. The bather must push a release button to turn the water over 37 degrees Celsius.
Temperature Limiter
There is a thermostatic control available that limits the maximum temperature of the water output, but doesn’t allow for precise temperature control. There is a maximum temperature limiter on most pressure balance valves, but if you turn up your hot water tank or don’t calibrate the set point of the maximum temperature, you could still get scalding water out the fixture.
Temperature limiters on shower valves are a common code requirement. Many shower valves have this built in. When installing the valve, the temperature needs to be properly calibrated with a thermometer or your shower may be able to get too hot or not hot enough. Some area plumbing codes require all non-thermostatic bathtub valves to have temperature limiters, alternatively, temperature limiters are also available to install at your hot water tank to limit the temperature to all the water in your home.
Pressure balance
The mix between hot and cold must be adjusted every time you use the faucet/shower and there is no anti-scald protection. The water may get very hot or very cold if other water is run in the house at the same time as you are showering/filling the tub. i.e. when the water gets hot when someone flushes the toilet. A pressure balance valve needs to have the temperature adjusted every time you shower or fill the bath. The pressure balance valve tries to keep the balance of hot and cold the same each time. The pressure balance shower valve senses that there is less cold water coming through the supply tubing and into the shower valve, so in turn it reduces the amount of hot water coming through the valve to maintain the same hot-to-cold ratio through the valve. There is a slight delay in this response.
Which one should you use?
If your main concern is price, then the pressure balance valve is more economical.
If you live in an older house with wonky plumbing where you notice a drop in water pressure out of the shower when flushing a toilet, then a thermostatic valve may be the better choice.
If you have trouble feeling temperature changes due to diabetes, paralysis, MS, stroke, etc, then it is important to install thermostatic controls to help prevent scalding and you should turn down the temperature at your hot water tank as an added precaution.
If you want the best temperature control, or if you like to reduce the water flow out of the shower head when shampooing without changing the water temperature, then the thermostatic would be the better choice.
Make sure you check local code if you are using pressure balance fixtures to find out if you are required to have temperature limiters installed on your bathtub and/or shower.