Roseaukaine, unless your rifle is to be specifically a long range bean field type, a 4x12 seems to me to be a unneccessarly large scope for deer and other big game hunting.
I also agree with the other posters that said to go with the 40mm objective.
I currently have four Vari Xlll's and one VXll. All are excellent scopes but if I have the extra money, I'd go with the Xlll.

I have the new VXIII in 2.5-8 x 36mm it's a great scope. Out of the scoped guns I have it's the best, no question about it. All my scopes are leupold's ranging from the fixed M-8 compacts to the vari-x III. I haven't had the scope out in a hunting situation yet but it's first trip will be a bear hunt in June. I have shot it down the range on several occassions and even with the 36mm the light gathering capabilities are very good.
In my opinion you decided on the right scope with the 40mm instead of the 50. As stated earlier the 50 requires higher mounts making your sight picture not in line with your eye, causing you to search or creep for the center of the scope.(at least in my case). For fast target acquisition the lower the scope the better. If you have a lot of time to get on the animal, as hunting in a stand or over bait then I would say the 50 is fine. Just my opinion, the 40 fits my style of hunting a lot better than the 50. Maybe in someone else's situation the 50 is the best choice. It all boils down to personal preferrence. Leupold states in their owner's handbook, "The lower the scope the better". But on the other hand, they sell 50mm scopes!

You may want to look at the Zeiss Conquest. Slightly less expensive and IMO superior optics than the VX's. Bought a 3x9 Conquest last year and was amazed at the low light abilities and clarity. I would also stay with the 40 vs the 50 due to the additional height caused by the 50 rings. At lower power (3 for example), the exit pupil on the 40mm is 13.3. Most average older human eyes cannot take in more he 5-6, so a 50mm IMO is not needed. Just my uneducated guess. Hope this helps