A larger diameter objective lets you turn the magnification up higher and not lose the brightness of the image. A 56mm objective at 10 power gives you an exit pupil of 5.6mm which is about as much as the eye can use. A 40mm objective at 10 power gives you a 4mm exit pupil which is going to mean the image brightness is limited by the scope and not your eye, you'll have to turn the power down to get the brightness back and in doing so you lose some of the advantage the extra magnification gives you at last light. I've found the ability to use the extra magnification in low light is crucial to making a good shot. A shot that could easily be made at 4X in daylight becomes difficult as the light fades, being able to turn up the magnification and keep the image brightness is important when hunting last light. My main deer rifle has a meopta 3-12x56 with a #4 reticle, it's a great low light scope. I hunt mostly food plots in Mississippi where the good deer show themselves at the last minute if at all. I've made shots with it that wouldn't be possible with the standard 3-9x40 that lots recommend. I hunt from stands and don't care about the weight or the handling, I'm not hiking with it. It's a specialized tool that does the job it's intended to do wonderfully. Many on this board like to make fun of the "hubbles" but it mostly shows that they haven't used a really good low light scope under the situation it was built for, if they had they'd understand why they exist.
If you're really interested in a scope that'll take care of your low/bad light situations then take a look at the Schmidt & Bender 2.5-10x56 listed in the thread I linked. It's a fantastic bargain at that price, that scope is the cat's azz for what you're describing:
https://www.24hourcampfire.com/ubbt...le-your-choice-only-1295-00#Post12324054
