I would say that the toilets at Dubai airport T3 are of a very high standard in terms of cleanliness for a public toilet (better than London) on par with anywhere in the world.
If you are very picky you may want to pick a toilet with a little less traffic away from the central shopping area. There are plenty available so if you do come across a cubicle not to your standard there are plenty of alternatives.
A hotel room is going to be better but of course more expensive. There is also an airside hotel at Dubai airport if you don't want the hassle of leaving the airport and willing to pay the premium.
Hope this helps.