I breed both, I have limited amount of room and can breed more mice in the same square footage than rats.
I also need mice for my colubrids and I prefer to start hatchlings BP on mice, I get a better response that way.
As far as my adult BP they are on rats simply because I prefer to feed one prey versus 3 to 5.
Now when it comes to mice breeding if you have a good colony canibalism is as low as canibalism in rats.