Crushed coral is a good buffer. That's about it as far as benefits are concerned. There are more downsides, the biggest of which is that it serves as a trap for detritus and can cause elevated nitrate levels. Also, crushed coral is not a good substrate if you want to keep certain fish like some wrasses that "dive" into the sand at night, some sand sifting fish like Diamond Gobies and Sandsifting Starfish.
Sand, on the other hand, can be kept very clean by having sandsifters in the tank. If you want to, sand, if deep enough, can compose a deep sand bed with it's nitrate reducing potential.