Exit pupil (the term for what woodsdog was discussing) matters a ton in terms of light transmission. An 8x42 is going to have a 5.25mm exit pupil, and a 10x42 is going to have a 4.2mm exit pupil. Exit pupil doesn’t matter a ton in bright light because a larger exit pupil is going to end up being larger than your pupil adjusted to bright light. During low light, as your pupil dilates, the larger exit pupil in the binoculars is going end up being able to send more light and a better image to your eye. Despite both objective diameters being the same and physically being able to collect the same amount of light, the 10x42s end up transmitting less light to your pupil and you end up losing out on detail.
There’s a limit to it based on the size of a human’s pupil (which gets smaller as you age), but all things being equal I’d take the binos with the larger exit pupil, particularly for hunting. I generally try to look for a 5mm exit pupil as it does a better job matching the size of your pupil in low light.
Obviously the quality of the glass matters, as does the type of prism in the binos.
For most whitetail applications, I’d recommend an 8x42. I have Maven B6 10x50s and I’m probably going to add a pair of the Maven B1.2 8x42s to the stable. The 10x50s are phenomenal, and when I’m hunting big ag fields and such they are great, but in the big woods VA hunting I now have to do the 8x42s probably make more sense.
I’ll say this about glass - you’re going to spend more money in the long run by buying cheap binos off the bat. Save for a while if you have to, but you’re better off buying a set of Maven B-series or Vortex Razors. Optical quality between the two I mentioned and something like the Diamondbacks isn’t even close.