I would run both UV and carbon. I've done it for years on my FO setups and always had crystal clear water. When I set my reef up in November, I added carbon and UV to the setup and you can't even tell there's water in the tank. I recommend both!
You can get away with a small wattage UV on your tank. On my reef(125g) I'm using a cheap Coralife 18w. I'm not looking for parasite control, but rather to kill free floating algae... thus I don't need a big wattage UV. If that's your goal, then you can do the same.