my statement is down to personal experience, but after a little reading I believe this to be the reason, ozone is more reactive than h2o2 which means it oxidizes quicker and is more intensive. Its just better at sterilizing. It kills not only more microbes but a wider range of microbes, it also destroys the most resillient of bacteria.
plus the way i always used h2o2 was to pour it into the res, at which point it starts to dissipate. As a grower you don't know what happens after that, is it enough? You don't really know. With an ozone generator connected to the venturi part of your pump you are constantly pumping in o3, you can do this for as long as you like, I've ran it for 12 hours in between res changes. I still use bleach in with the solution but the ozone is what I rely on to kill EVERYTHING.
They use ozone to sterilize medical equipment, you can take that to the bank.
hope this helps