Rim-to-rim is special because it covers both north and south sides of the Grand Canyon. It also requires special arrangements for transportation.
A Rim-to-River (and back) hike from the north would be more extreme than R2R, due to the additional elevation and distance compared to the R2R. Rim to River on the south is done by a lot more people, and it can be done on two trails, so you don't need to return on the same trail.
