I'm thinkin' this varies by the observer, by the eye-brain combo of each individual.
...when some low surface brightness object or the dim mag 13+ stuff will have me go back to mono-viewing, but not yet.
There's no argument about the physics- the light pokin' thru each half of a BVer will be less-bright than before it was "split". But the summation-effect... THIS is what varies person to person!
For me & my eyes+brain, i'm convinced that brain-summation nets me essentially all what was "lost" in the optical splitting. I've gone back & forth b/t bino & mono, same or close magnifications, and it's a rare event to see mono what i can't see bino... it's down to percentages of time a faint star is seen- 50% in/out averted versus 75%. That close!
Yet for others i'm sure they've found differently. And some of that might be aperture-dependent?... a small scope showing the difference more profoundly? I dunno... haven't tried BVing anything less than 10-inches. 'Tis been 15-inches the past five years...
My experience is that bino reduction in deep sky brightness is more apparent with smaller scopes. I’ve gotten to the point where I only use my Denk II for solar/lunar/planetary with my 5-inch refractor and 6-inch reflector. I find the reduction in deep sky brightness too objectionable on these scopes, where I’m pushing my 5-inch APO down to mag 12 galaxies from my front lawn. On the other hand (other scope?): I use the bino 2/3 of the time with my 20-inch Dob. The main reasons why I would not go bino with the 20 are: not enough time to put the bino together or I’m dealing with a lot of ‘public’ or Newbie friends.