"Advantages" is perhaps a loaded term, but there are, generally, some differences.
Start by thinking about the differences between a 34" scale bass and a 35" scale bass. Now go the other direction. Do that twice for a medium scale (~32") bass, and 4 for a short (usuall 30-30.5", but there are a few even shorter).
So: shorter reach (which for some people means cramped fingerboard), less string tension at a given pitch, typically fatter, flabbier, woofier sound (though electronics are gonna muddy those waters...or UNmuddy them, I suppose...)
Overall, despite sitting right in the middle, I find my 32" scale bass to FEEL closer to a 34" than a 30". Can't explain it, but it just doesn't feel like a huge difference, whereas going to a Short Scale is always more noticeable. That said, flats on a 30" is one the the half a dozen sounds that I consider to be Top Tier go-to bass noises. Whatever it is that people mean when they talk about "piano tone," flats on a short scale is the polar opposite.
So educate me on the advantages of having a short scale bass?