The main advantage is higher efficiency. In a nutshell, a short time before milling the grain enough water is sprayed over the grain to wet the husk and make it more pliable. This allowes a finer milling without tearing the husk. Obviously you'll have to change your mill settings with less gap for a finer crush to take advantage of this.
My method is to spritz about 3 oz of water over grain for a 5 gallon batch with a small spray bottle, mixing the grain around while doing so. I then let it set about 10-15 minutes while I heat up my mash water. You'll have to experiment a little. After the grain has set it shouldn't really be visibly wet and the husk should have soaked up all the water. After it has done so, I mill the grain. Another self-check is looking at the rollers when you're done milling. If you have much more grain stuck in the rollers than normal or if the rollers are wet then reduce the amount of water or increase the time... you'll have to find a balance. Anyhow, just from my observations, I get better efficiencies with a finer crush but almost all of my grain hulls are completely intact for easy lautering. An added benefit is less grain dust at milling.
FWIW I'm using a Barley Crusher-ish mill with rollers, I'm not sure if the same would apply with the corona-type mills. Hopefully someone will chime in.