Unbreakable said:
though it's amusing that we are choosing the more "cute" animal when we did the opposite for bunny -> rabbit for that reason.
It's probably a mix of the greater negative connotation tied with the name rat than with mouse and the help of a certain well known mascot with his fanclub having "mouse" eared hats that has resulted in mouse being preferred over rat naming. Of course when it comes to naming between mice and rats, it's about size. As mice are the smallest, and rats are everything larger... one would assume a person with those ears and tail would thus be classified as a "rat."
If someone really wanted to dig for a term for both, then murine apparently would be it. As a noun it typically refers to any member of Murinae (ie Old World rats and mice), and as an adjective refers to anything pertaining to or is characteristic of rats and mice. Although apparently there is a product called Murine Ear which is an ear wax removal product, so that'd be awkward. Anyways, +1 to combining the two groups, regardless of the name we toss it under.