First let's look at exit pupil math. Exit pupil is the amount of light coming through the scope and is subject to the magnification vs Objective lens size. For instance; a 6 power scope with a 42 mm Obj, yields a 7mm exit pupil. Most adults can use most of this exit pupil, but not all of it. Therefore the picture will be bright. say you then change magnification up to 7 with the Obj of 42, the exit pupil would then be 6. Most of the exit pupil falls into what a majority of healthy eyes can take advantage of, and hence it would appear just as bright to most users. This is because most of us that are beyond our early twenties, can get our pupils to dialate to around 6+/-. When the exit pupil drops below what our eyes can take advantage of the picture becomes less bright.
The advantages of a larger objective, are ability to use a higher mag range in low light. Resolution is better in a larger objective scope, provided all other things between the scopes being compared are equal. Also lens coatings are a large percentage of a scopes ability to transfer light. Avoid saying "light gathering" as that is a selling phrase, and not actually accurate.