This is one of those questions which will get multiple answers.
The thing is.....what are you trying to do?
You are trying to clean an uneven surface. Therefore you will need a scrubbing machine with a brush that will get into the nooks and crannies and also the grout.....in other words a polyprop brush attached to a rotary.
Then there is the cleaning solution. Probably anything will do it. I have used ph13 strippers to Prochem powerburst.
Yes powerburst works admirably on stone floors. Did you ever spill some on a custys floor and feel embarased that it had left a clean patch after wiping it up? I only ever used that on the spur of the moment

After doing loads of these floors, I would reccomend Lithofin Wexa. It's a solvent cleaner at about £12 a litre. I guarantee it will bring your custy's floor up like new. I'v probably done what seems like 100 of these floors but probably at least 50 and each one has come up like new