Just from my experience, the biggest issues I've seen with UV is that generally speaking the units are under sized and don't allow enough contact time to do the trick. I've had and have heard others having a lot of leaking gasket issues allowing water into the quartz sleeves the bulbs rest in.
I like ozone for bigger systems due to the ability to sterilize 100% and still off gas prior to the water hitting the tank - meaning you're getting everything you need. From my experience ozone is also cheaper long term.
We run both right now at the aquarium. Our new touch pool runs both UV (750watts) and O3 injection to keep it clean. For treating incoming water from the bay, we use ozone injection and run the ORP up over 600 mV for 24 hours to insure 100% sterilized water before it goes into the display.
When I said UV is good to keep clean systems clean is that UV is good for killing off most of the eggs of parasites, but at the levels used in most aquarium situations it won't kill any other stages in the life cycle. So if you have an outbreak or are hoping to use it in a quarantine situation, you're still going to have issues. Ozone is adjustable, and you can kill off anything in the water column if need be.
Each does have it's pros and cons for sure.