Your car (if it's an 89) already has a Traction-Lok rearend -- you already have posi. If it's not working (symptom is just the right rear tire spinning when you smoke 'em), a shop can rebuild the traclok unit without removing the differential.
A wet nitrous system adds the additional fuel required with separate injectors nozzles for fuel. These typically are installed somewhere downstream of the throttle body in the intake manifold. A dry nitrous system senses when the nitrous is activated, and typically elevates the system fuel pressure so that the additional fuel required is supplied by the car's existing injectors.
With either system you need to be certain you have enough fuel pump to meet the cars needs for fuel. Running lean with nitrous usually results in catastrophic failures which are neither pretty or cheap to repair. Depending on how big of a shot you're running, with a dry system, you may need to switch to larger injectors to have the capacity to provide enough fuel for the extra oxygen provided by the nitrous. Of course, with that larger injector comes the need for a recalibration of the maf or ecu to accomodate the larger injectors.
The downside of a wet system is puddling of fuel in the intake, and the possibility of an intake explosion as you now have fuel mixed with air in the plenum. The upside is you usually don't have to worry about whether your stock injectors have enough capacity to provide the additional fuel needed.
The downside of a dry system is being sure you have enough injector capacity to supply the additional fuel, and being sure your calibration for larger injectors (if you must do that) is good so that drivability/efficiency are preserved when you're NOT using the nitrous. The upside is better mixing/vaporization of the fuel that's added since it's coming in via the injector, and no chance of puddling of fuel as could occur with a wet system.