A pressure balance valve would sense the reduction in pressure from the cold side and lower the hot water to compensate, reducing the ultimate volume on both feeds.
A temperature sensitive valve needs to react to the difference in temperature caused by decreasing the cold flow, dropping in temp of the hot side, or decreased temp of the cold supply. It does this by either reducing the hot or increasing the cold, ultimately producing the same effect. It has the added benefit of adjusting the outputs automatically as you use up the hot water in the WH tank, stretching the time the temperature remains constant until it's running all hot (which may be cold by then). WIth a pressure balance valve, as you use up the hot water, you'd have to be adjusting the valve to keep the temp fairly constant since the pressure wasn't changing, the temperature(s) of the supplies are.