A 50mm scope will let in more light, but your eyes cannot use it all. The average human eye will only open up to 5mm. If you divide the scopes front objective in millimeters by the power setting you determine how many millimeters of light are coming through the scope. A 50mm scope set on 10X lets in 5mm of light, all the light your eyes can use. Any more is wasted.
A 1-4X20mm scope set on 4X or less will appear just as bright in low light as a 3-9X40mm set on 8x or less, and the same a 4-12X50mm when set on 10X or less. And this assumes scopes of equal quality. 50mm glass costs a lot more than 40mm. A 50mm scope of equal quality will cost $50-$100 more. If you are paying about the same for the 50mm scope you are getting a lower quality scope. I will guarantee a Zeiss Conquest, or Leupold VX-2 or VX-3 with a 40mm lense will be much brighter than a Simmons 50 mm scope. And you don't have to spend a fortune. There are a lot of decent $200-$300 scopes with 40mm or smaller glass that will do all you need to do legally.
If you need more than 8X of scope power a 50mm scope will offer a tiny bit of useable light transmission, but only between 8X-10X. If your power setting is set at 8X or less it won't do a thing a 40mm won't do. If you need more than 10X, you need an even bigger scope. I can make hits on deer size game at 400 yards easily with a 4X scope. That is as far as I need to shoot in any light so I have no need for more power or bigger glass.
The negatives far outweigh any positives. If you buy cheap, big glass you won't see anything. I also hunt in some pretty thick woods right up till dark, 30 min after sunset, and can still see well enough to make hits several minutes after legal shooting time with any of my 20,32, and 40mm scopes.