"Twilight factor" is key to performance in dim light.
The quality of the coatings is much more important. A Zeiss 10x56 would have a twilight factor of 23.66, a Leica 12x50 would have a twilight factor of 24.49. From my own experience, I would get the Ultravids for low light, because their coatings work very well to enhance the contrast of dark shades and colors in dim light.
But I would not get a giant binocular like that. I have an Ultravid 10x42 and it is all you can ever need for hunting. I never felt that they should have been brighter – I used them to count sandpipers under full moon, they should work for hunting.
You sometimes see "twilight factor" listed in a binocular description, as a measure of the resolving power in dim light. This term was more important years ago, before modern optical coatings were invented, than it is today.
Twilight factor is a mathematical formula that shows how both the size of the objective lens and the magnifying power contribute to a binocular's ability to show detail in dim light.
The twilight factor is the square root of the product of the diameter of the objective lens and the magnifying power of the binocular. [For example, an 8x32 binocular would have a twilight factor of 16, and a 10x42 would have a twilight factor of 20.5.]
However, in a modern binocular, performance in dim light depends more on the quality of the optical coatings than on the twilight factor formula. Good coatings can double the amount of light that gets through the binocular.
If you pick up an old binocular from the 40s, or a cheap, low-quality binocular, you'll see very poor performance in dim light. Then look through a modern, top-quality binocular with the same magnification and lens size, and see how much brighter and clearer the image is, despite the fact that both binoculars have the same twilight factor rating.
So if you're looking for good image quality in twilight conditions, you shouldn't just rely on the twilight factor number. You have to take the quality of the coatings into account.