I seriously doubt exposer would be less. The Moon has no atmosphere and the work they plan on doing requires hours on the surface away from the base or the rover or camp.

They also plan on having people walking around in the permanently dark areas which approach absolute zero.

One of the speakers at my Spacesuit Symposium was Irene Schneider who gave a talk called "Characterization of the Radiation on the surface in View of Future Human Presence" which was about the lack of good radiation data for Mars. She was counting on Mars Science Laboratory Rovers to give us actual surface radiation data (RAD PDF). I tried to explain to her that MSL very probably would be either delayed or canceled.