I believe that the difference the shutters make is that with a rolling shutter, you may get smears or breaks in the image when recording a stream of something that is in motion (either the camera moving or the object it is looking at). An example where a global shutter is better than a rolling shutter is attaching a camera to a balloon and floating it up into the atmosphere.
A rolling shutter would not be suitable for tracking very fast objects such as using it in a self-driving vehicle to detect other vehicles and pedestrians.
It is hard to say how fast is too fast before an image taken with a rolling shutter starts breaking up. So if you plan on recording movement of any kind, I would err on the side of caution and go with the D435.