Having dicked with a dry sump on a CFC I'll give you my $.02 in order of decreasing importance.
Advantages
1. Oil pump always has a steady supply of air free oil that is not effected by g-forces.
2. Allows engine to be mounted as low as possible in the frame.
3. You decide how much oil you want in the car (as little a 3 qt to a 55 gal drum if you wanted.
4. You decide what pump, how fast you want to spin it, and where you want to scavange from.
5. Little or no oil in the sump eliminates windage for more HP at high rpms.
6. It looks cool
Disadvantages
1. Cost
2. Weight
3. Leaks
4. Additional maintanence
5. Complexity (more of everything like hoses, fittings, etc.)
IMO without a doubt the best way to oil your engine on a car if you race. If it was legal in IT my car would have one.