Dry Shot = Nitrous ONLY, your existing fuel system has to be up to the task of supplying enough fuel for the shot. If you're fuel system is up to the task (and the motor will run rich when not on the squeeze) a dry system is almost a fool-proof setup. Very easy to just throw on and go.
Wet Shot = Nitrous AND fuel in the spray. As long as your pump is up to it, wet shots are easier to tune as you can put the amount of nitrous you want through the engine and then just adjust the size of the jet on the fuel side to get the proper air/fuel ratio. Wet shots "hit" harder than dry shots do, and as a result usually produce a little more power and quite a bit more torque. The biggest disadvantage is the need of an aftermarket high flow fuel pump to supply enough fuel for the "wet" side of the nitrous, and the risk of the mixture puddling in the entire and shooting a fireball out of your throttle body.
In general, if you feel comfortable running either shot, a wet shot is better IMO. It'll yield better results, and as long as you dont have a puddling problem (pick a good injection point), it's safer against detonation since the system supplies the right mixture of nitrous AND fuel to the engine.