Hello,
From what I can tell, they perform the same action. As long as you have the Update Surfaces turned on, any command you do in the Geometry>Curve from Surface menu will imprint the newly created curve onto the existing surfaces. This is the exact same thing that the Geometry>Midsurface>Intersect command is doing. If there were any differences to point out, it would be that the Geometry>Midsurface Intersect command allows you to select more than two surfaces at a time, making it quite a bit more robust.
Mitch