Having done a bit of experimenting, taking indoor shots with my 5D in the evening, of smooth surfaces that show noise, I'd say that stacking in mean mode is equivalent to a 2 stop ISO advantage.
In other words, 5 hand-held shots at f4, 1/50th and ISO 3200, after stacking and auto-aligning, produce an image with the same degree of noise as a single shot at 1/13th and ISO 800.
Considering that ISO 3200 on the 5D is equivalent to ISO 1600 underexposed one stop, I find this result impressive.
Within the shutter speed limits I consider adequate for a particular shot, I can now stop down 2 stops for greater DoF, without getting the increased noise I would expect without stacking.