Both.NorthForkSportsman said:
The width of the objective, divided by the magnification, gives you the "exit pupil". You might have noticed that when you zoom a scope that's further away than the eye relief the dot you see gets smaller. The image is thus dimmer. Note that once the exit pupil is larger than your pupil it stops getting brighter.
Good coatings increase how much light ends up going through the lens rather than reflecting off.
So this means that a good 7x35 binoculars can be brighter than a cheap pair of 7x50s. Indeed, I have some nice Nikon 7x35 fully coated binos that work better for star gazing than my cheapy 7x50s. The coatings make a difference. Also, in my back yard, which isn't that dark, and my eyes don't dialate as much as I've aged.