They lose a lot of light, but mainly because they spread it everywhere and the amount that gets bounced back to the subject varies enormously according to the surroundings.
If you use a Stofen outside* where there is zero light coming back, the small amount that goes direct to the subject is dramatically reduced - like several stops.
*Edit: also, because there is no light coming back from surrounding surfaces outside, there is zero softening of the light either (Stofen doesn't actually make the size of the original light source any bigger).