Disclaimer - I should mention that my answer only applies in the context of the original question. I'm discussing my experience rappeling in a rock climbing context, using a dynamic single or half rope, a "stich-plate" or tubular belay device, and an autoblock backup (not a prussik). I can't speak to rappeling in caving (where the gear would be different) or in rescue situations (where you'd be rappeling with the weight of 2 or more people)
Actually, rappelling down a wet rope is about the same. Its just that everything else in climbing becomes more dangerous when its raining. :)
I live on the east coast of the US, and we get rain pretty frequently. There's about a 30% chance of scattered thunderstorms nearly every day, and rain is just a fact of life. I get rained off a route maybe once a year.
While I can't say I enjoy it, actually rappelling down a known rappel route in the rain isn't all that bad, especially if you can stay tied into a rope system the whole time (i.e, you don't have to scramble unroped along a ledge to get to a rappel anchor).
The rope dynamics don't seem to change all that significantly. I always rappel with a regular tubular belay device and an auto-block backup, and I usually rappel with the device in "high friction" mode. (note - I also use a 9.8mm or thicker rope) I would think that the rope would get slipper-ier, but it seems like the ropes get thicker and heavier when they're wet, so maybe that counteracts it some (my rope is supposedly "dry treated", but gets fatter anyway).
What is more dangerous
- Rock becomes slippery - scrambling and climbing are more precarious. Lichen that might otherwise be dry become moist and slick.
- Cams might become unreliable. This may just be an incorrect anecdote, but I've heard from other climbers that cams (which rely on friction to grip the rock) can't be counted on
- Some kinds of sandstone (esp desert sandstone) becomes fragile when its wet.
- dynamic ropes lose some of their elasticity, so lead falls become more hazardous.