Advancing the film manually always means bringing the camera away from your eye, even if only for a brief instant, and that can mean the difference between getting and missing the shot, especially when one is photographing time-sensitive subjects.
However, motor-driven cameras are always ready for the next shot.
I have motors on all four of my SLRs for that very reason. I virtually never shoot "machine-gun" bursts, as I don't find them necessary for my subject matter, but the ability to always have the film advanced and the shutter cocked and ready for the next shot is an absolute necessity.