It is funny that there are so many answers to this question without getting one that has to do with the actual function of a shower valve.
Let's go over the 3 examples that we have as examples already:
This shower system has electronic mechanisms to calibrate the temperature and flow. The pros include easy user interface, looks cool (maybe because its different), and allows user to turn a little knob.
The cons are many though. First this must be calibrated correctly. After calibration the systems hot/cold water flow is changed it will become uncalibrated. Also what if you favorite temperature is between two of the settings? Now you are either a little too hot or a little too cold. And then the most obvious thing is cost/repairs. The low end ones I have seen are $500 plus compared to $50 for a more traditional setup.
I kept the image even though a don't agree with it. Most modern versions of this have a decent size comfortable zone and this is adjustable. Note that in the application the water will divert through one valve like, the same as example 1. The water will be mixed together before being shot out. The pros include familiarity, ease of use, and the ability to tune your temperature tighter.
The biggest con with these is that most do not come with any sort of flow rate control. It is either on or off. The anti-scald mechanism is another feature that these have and not sure if it is a pro or a con - to some it will be one and to others the opposite. I for one like to be able to set the temperature as high as I want - especially useful when cleaning. The last con also has to do with the anti-scald mechanism. When the flow rate is decreased (think toilet flushing or someone doing the laundry) the valve will automatically process slower to reduce chance for temp changes. Which means you get a limp shower for a few minutes.
3. Good old knobs. The key to the knobs is that they do not (normally) have a shared mixing valve. Each operate independently of one another. The pros include they are cheap, they are intuitively easy to use (other than some people have hot on the left), only with knobs can you get the EXACT TEMPERATURE AND FLOW, and they are easy/cheap to install.
There are many cons on the knob side either. Some may say how they look, but I have seen some cool knobs. Another would be that you have to turn two separate things. If you have children the fact that there is no anti-scald mechanism is a con. Children can turn knobs and burn themselves easier. However the fatal flaw of the knobs is that you don't know what you get until you get it. You turn the hot and cold and just guess that the temperature might be right. You feel the water and adjust until it is right and continue to do so every shower there after.
Which is the best? Each of these choices offers different levels of work, different levels on install money, and different levels of controlability by the end user. Like any UX question, design should not trump functionality.