My road bike has carbon wheels. I have many, many times been caught out in the rain on this bike. Basically if it's wet out, I have no brakes for at least 4 or 5 seconds after I first apply pressure. It takes that long to even begin to slow the bike down. Not that big a deal on the flats except that I have to remember to plan ahead for stop signs etc. or else I'll roll right through them. I have no recourse basically if it's an emergency situation. On hills it's really bad. I can end up going 30 or 40 yards down the hill before I get any braking at all. Wet conditions are really the only case where I think I would prefer discs, but that's a pretty big "only" if you ride in the rain at all.

I have a new gravel bike that has disc brakes. I haven't yet had the pleasure of riding it in the rain. I'm not looking forward to it, but I sort of am.