Re: 50mm vs 56 mm Help.
What a bigger objective buys you is being able to dial up the magnification a little further before the image starts getting darker.
Once the exit pupil of the scope (which at the relevant magnifications is objective size divided by magnification, so it decreases with increasing magnification) gets smaller than your eye pupil, the image gets darker. Now as long as the exit pupil of the optic is bigger than the eye pupil, there will be no difference in image brightness, so at lower magnifications there will be no difference in brighness.
Assuming that the eye pupil opens up to 7mm (this varies greatly for different people and decreases with age, 7mm is an average value for a younger person), the "brightness threshold" is at ~7x for a 50mm objective and ~8x for a 56mm. At 7mm, there will be no difference in brightness, same for higher magnifications and bright daylight, where the eye itself limits the amount of light by adjusting the pupil size.
That 7mm average value and the technical data of common low light optics is also the reason while people believe that you "cannot use more than 8x at night". 56mm/8=7mm, so a 56mm optic will produce a 7mm exit pupil at 8x magnification. First of all, not everyone's pupil opens that far even under low light conditions, so if your pupil only goes to 5mm for example, you may as well crank up the magnification to about 11x and enjoy more magnification (=better resolution/detail recognition) at the same brightness level.
With any given maximum eye pupil size, a bigger objective lens will let you dial magnification a little higher before the disadvantages of a darkening image outweigh the advantages of higher magnification. Where that threshold is is something everyone has to find out for himself.
All else being equal (impossible to tell whether this is the case without insight into the engineering, so this is just for the sake of understanding of general tendencies), the smaller objective scope will produce a better image in good light conditions because optical aberations increase with bigger objective size at a given focal length.
An exit pupil that is bigger than the eye pupil will allow for more "misalignment" of the eye behind the scope, making it easier to pick up the sight picture with a sloppy cheek weld and generally making the view more comfortable.
Again, in a nutshell: Bigger objective = more usable magnification in low light conditions, no difference in image brightness below a certain magnification threshold, no difference in image brightness in daylight unless extreme magnification is involved.