I can't offer first hand feedback, but I have read a ton of reviews and comments mostly here on Rokslide.
My conclusion (from reading) was that knowledgeable folks with experience with both indicate better light gathering with the 50's. Apparently the difference is measured in minutes of additional use at dawn and dusk - I think less than 10. This view seems to be consistently held.
Same result based on spec comparison.
My experience with alpha binos includes an ancient pair of 10x42 SLC's and new pair of 12x42 NL's. At one time I had a pair of SW Poro prism 10x50's. I loved viewing with those massive 10x50 binos, but hated the size and weight. About 30 years ago SW swapped them out on warranty for the SLC's. I prefer the SLC's based on size and weight (backpack hunting at 10,000 feet) but I always felt that the older 50 mm porro prism design had superior image quality. I never had the opportunity to test them side by side, but I immediately felt like I gave up "something" when I switched to the 10x42's.
In speaking with SW recently they suggested that the simple fact of having a 50 mm objective improves the overall visual clarity - vs. a smaller objective, and that my gut feel that the old Porro prism binos' had a better viewing experience was probably accurate (vs my old non-hd SLC's). That wasn't your question exactly, but thought you might appreciate the perspective.
Personally, due to my style of hunting, I put less value on first and last light glassing, but I put a lot of value on image quality and I have a biased towards smaller form factor and lower weight. Despite my penchant for the smaller form factor and lower weight of the 42's, I sometimes find myself thinking that perhaps better image quality is a good reason to go with 50's.
I don't believe that NL's are available in 50's yet, so the comparison on image quality (not your question, I know) might be the 50 EL's vs the 42 NL's. That comparison would be interesting to hear about from those who own both.
I think when it comes to your original question - pure light gathering - the question is settled - the EL 50's win by a nose (based on what I've read on Rokslide and elsewhere).