No, they are nothing alike in reflector design. The Eiger has a smaller reflector and on my medium version it also has a diffusion screen.
You're right, it does not look anywhere near as deep as the MS reflector.
EDIT: Now that you mention it, the medium's optic and beam (at least in that one shot) totally remind me of the Princeton Tec EOS, a beam that I LOVE. I just may get the medium.
EDIT 2: From the shots RobynS posted comparing all of the different tints and beam shapes, the medium looks like it doesn't have as wide/bright of a spillbeam as the narrow are my eyes just bad? These shots also look like the EOS.