I find rats are DON'T stink the way mice do. I don't care how clean you keep a mouse cage, mice stink.
Of course if you let a rat cage get too dirty and urine saturated, let food rot in it, leave spilled water in it, etc its going to stink but with reasonable cleaning & bedding changes, rat cages are practically odorless.
I hadn't raised rats until the past few months and was surprised how different rats are from the other pet rodents. Rats are so obviously much more intelligent than other pet rodent species.
I was surprised to find out how clean and odorless rats are, because except for handling a pet rat in school, my experience with rats had been in dealing with living in a farmhouse and trying to keep wild rats out of the house and dog kennels. Wild rats were so dirty! You could tell where they had been running because of the greasy body tracks they left on the ground or walls.
Another species that is odorless and puts out very little urine is the gerbil, because they are a desert rodent. I used to raise many color varieties of gerbils and in a room full of gerbil cages kept adequately cleaned, there was no stink.