Given equal quality of glass and same magnification the 50mm allows a larger circle of light transmission to the pupil of the eye. Known as "exit pupil".
Exit pupil in mm = diameter of the objective lens divided by the magnification
With a 9x50 scope the exit pupil is 50/9 = 5.6 mm (more light),
compared to a 9x40, 40/9 = 4.4 mm (less light).
There is a practical and functional limit to this advantage. When the exit pupil size exceeds the actual diameter of the pupil the eye cannot use the additional area. So somewhere around an exit pupil of 7 you will achieve the maximum amount of light possible.
I disagree with most of you on the 50mm. I actually like the 50's better.
As far as the comments on the large objective scopes being more subject to damage.....I guess the nightforce scopes probably won't hold up as a majority of those have large bells. Don't buy a POS scope and you won't have to worry about either size.
And my 50mm scopes are mounted on low rings....so it's mounted at the same height as the 40's.
I like the bigger objectives too. You won't miss them until it's last light and you have a monster out in front of you. As far as the 40 mm being more durable I have to wonder what some of you do to your rifles out in the field?? Each one has its merits, so personal preference is what wins. Good luck with your VX-R, they are great scopes.