The most important consideration is lense quality. Good glass trumps large size every time. The size of the objective along with magnification determine the diameter of the light beam leaving the back of the scope. Lense quality determines how bright that beam of light is.
If you divide the scopes objecitve size by its magnification you get the exit pupil rating. This is the diameter of the light beam as it hits your eye. For low light you need an exit pupil rating of 5-6mm. Most peoples eyes cannot use any more. An exit pupil rating of 6 or more is wasted. A scope with a large objective will allow you to use it on higher magnifications, but unless you really need 10X or 11X you gain nothing over a 40mm scope set on 8X. If you never need more than 4X, then a 20mm scope will be just as bright as a 50mm lense set on 10X. Assuming equal quality glass.
As long as you stick with the better Leupolds, Nikon's, Burris, Zeiss, etc, the difference is actually quite small. In my experience Zeiss is slightly better than the others I've tried, but any of them work well enough for me to shoot until several minutes after legal shooting time has passed anyway. The fact that the Zeiss lets me see for 5 minutes longer into the evening isn't of any practical advantage.
If you have a choice between a Zeiss and a Barska, pick the Zeiss.
If you're choosing between two similar scopes, with different sized objective lenses, in low light when your pupil is dilated, you want the bigger objective.
Adjust the magnification so the exit pupil of the scope is about the same size as the entrance pupil of your eye. The bigger objective will get more (brighter, more densely focused) light to your eye.
You want good glass, and you want a good ratio of power to objective size for the max exit pupil the eye can take advantage of. The more power, the larger the objective you need. This is one reason many people like low power for hunting scopes. I have a 2.5X8X36 Leupold Vari X III on my .308 and a 2X7X32 Vortex Viper on my .35 Remington.