Certain movements are better executed than others and depending on your needs for a watch, a movement may or may not support those needs with its complications. Things like day or date complications or chronograph features for example. Things like power reserve will determine how long your watch can sit unworn before it stops. If a watch won't last overnight it can be a pain to reset it every single morning.
Next, I often look to see how serviceable is a movement by your average watchmaker. This is very important if you plan to keep the watch forever. How easily can parts for the movement be found and at what price. There are some movements that are so difficult to work with that it's cheaper to just replace the entire thing than to have it serviced should someone go wrong. Movements like the Seiko NHs are great because you can find the parts or the entire movement easy. In-house movements for microbrands may be more difficult to service.
After that, other considerations are quality of movement. Some movements stutter instead of smooth sweep like they should. Some are known to die with a decent enough shock. Jewel count can be important in that case. For quartz, movements like the one in the Bulova Precisionist line are modern marvels because of the extremely high beat rate that enables a smoother sweep of the seconds hand then many automatics. Some movements are prized because of how thin they are which gives you the ability to have an ultra thin watch.
Finally, some movements are just damn beautiful to look at in a display case back. My favorite cheap movement is the Seagull ST19 series with its gold, blue and fuchsia accents. The finishing of a movement on a high-end watch is fascinating to me because of the precision and detail on such small parts.
Overall a movement can persuade or dissuade me from a watch purchase. I'm always looking to find a watch with a movement I don't already have in my collection just so I can observe how it functions.