A quat or any disinfectant may kill the bacteria that cause the odor, but unless the source is removed (the urine removed by cleaning), there are plenty more bacteria that will eventually start the decomposition of the urine again and the odor will return.
An oxidizer will work faster than enzyme product, but it requires the use of a lot more moisture. If there are a lot of stains to deal with, all that moisture could be a problem for wood / particle board / OSB subfloor.
In the long run, I think the enzymes will do the best job. But they will not work as fast as an oxidizer.
I have written a training manual on how to successfully deal with urine. Printed versions sell for $10. But I will email a copy to anyone who asks for it.
scottw@bridgewatercorp.net Please, put urine in the subject line.