For bright stuff like the moon, it's my understanding the best way is take really high-speed video, hundreds of frames per second, then pick out the frames which has the least amount of atmospheric distortion and stack those.
So not only can you compensate for unwanted motion of the camera rig, but also for external factors like the atmosphere.
For faint deep-sky objects, IIRC you really do want long exposures, to overcome sensor noise. At least the comparisons I've seen using same total integration time, a few long exposures had much more detail and color compared to lots of short exposures.
That said, lots of short exposures might be all you can do if you're limited by equipment or such, and is certainly way better than nothing.