Most showers use a pressure balance shower valve that mixes hot and cold water at a specific but selectable mix, depending on how far you turn the valve toward hot or cold. This same valve also controls the flow of water to the shower head, so one handle is all you need. The problem I have with pressure balance valves is that they don't take into account the variations of hot and cold water during a shower and I end up adjusting the water temp 3x during a normal shower: 1) full hot to get the hot water up to the shower, 2) adjust cooler to get a comfortable temp, 3) turn it up again when the hot water start to run low.
The thermostatic valve should use Ron Popeil's slogan, "set it and forget it". You simply set or better still "keep" the thermostatic valve at the temperature position you like and it does the rest. The valve maintains a specific temperature of water through variable supplies of hot and cold water, that simple. Of course, since this valve only controls temperature, not water flow, you need an on/off valve to send water to the shower head, another extra piece of plumbing, but within reason.
This post probably is only useful if you are beginning or considering a shower renovation, in which case, good luck, and I hope you find the thermostatic valve experience as great as I have.