A UV system for an outdoor residential (low bather-load) pool exposed to sunlight makes no sense. As Ben noted, there is reasonable use for UV in indoor pools mostly to help break down or prevent combined chlorine formation, but UV is not a general oxidizer and will not reduce chlorine demand. In fact, depending on the type of UV system you get, your chlorine demand could go up somewhat. It is not a bulk-water sanitizer so you can't lower your FC level (FC/CYA ratio, to be precise) as a result. No circulation-based disinfection system, be it UV or ozone, does anything against pathogens or algae growing on pool surfaces; this is why a bulk-water disinfectant such as chlorine is essential.

It is true that the wavelengths used for UV systems are different than that from the sun (whose UV drops off rapidly below 300 nm due to atmospheric absorption), though again how different depends on the type of UV system you get. This link gives some useful basics about the different spectrums of UV. Note that hypochlorous acid is degraded by UV from <200-350 nm with a peak at 236 nm while hypochlorite ion is degraded by UV from 250-350 (and <200 to 230) with a peak at 292 nm. So medium/high pressure (broad spectrum) UV tends to degrade more chlorine than low pressure (single wavelength) UV.

In an outdoor pool exposed to sunlight, the UV in sunlight breaks down chlorine and in doing so produces hydroxyl (and chlorine) free radicals that are powerful oxidizers that help to oxidize bather waste that is otherwise slow to get oxidized by chlorine alone and the CC level is typically very low (usually <= 0.2 ppm and almost always <= 0.4 ppm). Also, bather load is low in residential pools. For these reasons, UV doesn't make sense for outdoor residential pools.

For indoor pools, the lack of sunlight exposure can lead to a buildup of combined chlorine (CC) so in this situation the use of a supplemental UV system can be helpful.

As for the disinfecting capability of UV, there isn't any need for that in residential pools since chlorine alone is effective against most pathogens, the most notable exception being the protozoan oocyst Cryptosporidium parvum. This pathogen is only introduced from the diarrhea of an infected person so is very unlikely to get introduced into your own residential pool. However, for commercial/public pools where one infected person can infect dozens if not hundreds of others, the use of UV to help reduce the likelihood of a major Crypto outbreak is reasonable.

There are also side effects of UV where it destroys some disinfection by-products, but creates others. I won't get into that here as this is still emerging science.