Actually, the benefit depends on the magnification and your age. For example, a 50 year old person has a maximum eye pupil size of about 6 mm in low light (i.e., for dark adapted eyes). As long as the exit pupil of the scope is larger than your eye pupil, the image will be as bright as viewing with the naked eye.
The exit pupil size is equal to the objective size divided by the magnification. For a 50 mm objective the exit pupil is 6 mm (i.e., the same size as the eye pupil) at a magnification of 8.3X. For a 56 mm objective the magnification is 9.3X at a 6 mm exit pupil size. At a magnification below about 8x both scopes have the same brightness for a 50 year old person. But at the same exit pupil size of 6 mm, the larger scope provides a12% higher magnification.
At higher magnifications, the ratio of exit pupil area to eye pupil area determines the brightness. For example, at a magnification of 12X, the smaller scope is (4.16/6)^2=48% as bright as the naked eye, and the larger scope is (4.67/6)^2=60% as bright as the naked eye. So, at 12X the larger scope is 25% brighter (as LouBoyd said).
If you do a lot of hunting in low light the larger objective can be worth the extra cost and weight.
