in a wet clutch, the metals from the 'dog teeth' or the teeth from the gears as they wear over time can pass through oil filters and possibly contaminate vital engine parts. At the same time dry clutch's don't have oil to keep it cool. Since a wet cluch reffers to a clutch mechanism being submerged in MOTOR oil. I would be happy with a dry clutch, as long as I don't clutchless shift my gears to death. But as ARA pointed out there is no major difference.
I would love to hear why Ducati choose dry or wet.