ozone is NOT an EPA approved primary residual sanitize. It really does not do a lot in an outdoor pool but can be of some use in an indoor pool as a SUPPLEMENTAL oxidizer. However, ozone is toxic so good air handling is crucial. Ozone mus be used with an EPA approved primary sanitizer (chlorine or bromine, bromine is not suitable for outdoor pools). Ozone can attack some plastics so it's use with vinyl liner pools is something I would question. ozone can actually increase chlorine usage since it tends to destroy chlorine.

Asking if you should use chlorine or ozone to santizer your pools ia an "apples and oranges" comparison. Ozone is a suppliment only and is not something that will keep your pool sanitized on it's own.

There are only 3 EPA approved primary sanitizers for pools:
Chlorine
Bromine (can't be stabilized against loss from sunlight so not a good choice for outdoor pools)
Biguanide/peroxide (expensive, works ok for a year or so and then becomes a money pit with such problems as pink slime and white water mold. Most people convert to chlorine at this point...just check the forum for the stories!)

EVERYTHING ELSE is a supplimental or unnecessary product and must be used with one of the three above.
This included ozone, UV, ionizers and mineral systems (which put metal into the water), enzymes, biofilm removinng products such as sphagnum moss bags (really? REALLY!?!), copper sulfate based products (copper sulfate is just an algaecide, not a santizer), magnets (these are not sold anymore from what I can tell but putting magnets on your pipes to 'magnetize' your pool water was one of the 'snake oils' that have been sold for pools just a few years back), etc.
Some of these supplimental products such as UV or ozone can be beneficial in certain installaions such as high usage commercial pools or indoor pools but don't do much for outdoor residiential pools and can actually cause you to need MORE chlorine and not less, others are pure snake oil.

Hope this helps.