Rockwool - cleaner, holds more water (I consider this a con, but some call it a pro), not pH neutral, comes in every size and shape, disposable, hard to underwater, easy to overwater.
Hydroton - dirtier (uber dusty), holds less water, pH neutral, reusable, easy to underwater, very difficult to overwater.
For those reasons, I chose hydroton, because you can flood the table more often, which to me means it's a more "active" system, which to me means more control/better growth/etc.
The best condition your roots can have is to be exposed to both moisture and oxygen at the same time (think of a fogger machine for DWC, aero, etc.), and hydroton allows you to put them in that state more often then rockwool (I flood for ten minutes every two hours, whereas in rockwool, I'd be doing about once or twice a day).
