To me a lot of people run spool or ball diff on carpet. However, it will really depend on your driving ability.
The 13.5s are not slow and as such a one-way is very difficult for a lot of people to handle consistently. If you can handle it, it should theoretically be faster.
On asphalt once you hit 19T most racers i know run the spool. I dont know about carpet but the one-way will get very difficult to control as you will have way too much steering on a high traction surface.