Tile floors are very common here in Florida. In my business, I usually use Meyer's Clean Day products, because they are safe, they clean well, and they smell really great. I dont use ammonia - the fumes can be toxic to you! Vinegar is great, but most of my clients want their homes to SMELL good, and vinegar doesnt.
The idea of using oxygen cleaning products is interesting to me and I might try it, but I would definitly add something else to make them smell good.
I read somewhere that old vinyl floors can be made to look nearly new by using Scrubbing Bubbles types of products, This one I want to try, when I get a home that has such a floor.