I hunted near 50 last year in late December. I would recommend 51 over 36A. Many of the roads will be snowed in, so unless you have a snowmobile you aren't getting far from a main road. I would also say camping maybe very challenging as last year it was routinely in negative temps for the high, Arco and Challis have some small hotels, they usually are filled up with hunters that time of year.
Finding Elk that time of year will not be hard, they will be in large herds down low on open south facing slopes, usually within a few miles or less of ag ground. Don't waste your time planning for or expecting a back country hunt that time of year as they won't be there.
Recommend 50 for late season access. Cow numbers are good in both (Fish and Game added more cow tags in 17/18 due to large numbers in pioneer zone) but access is tricky with snow. It started snowing during my 36a September archery hunt and my buddy got blocked out of a lot of good area due to snow fall when he drew the early rifle tag. Plus, the cows headed straight for the private land on the East Fork.
To clarify my answer above a bit more. I think 36a is good unit, as it is one I hunt. Lots of elk and good access, until it snows. Public land in the East Fork is limited until you hit the National forest at the end of the road. Prior to than much of the valley is private and blocks access to great swaths critter country. Prior to the snow I was able to use many of the trail heads to get great access. However, when the snow fell the Elk moved out of the timber and right down to the private. The access became increasingly difficult as we had to navigate up, around, and then down. Nothing more frustrating than just watching your quarry a couple hundred yards away but had to hike for two days to get around to them and hope they moved up.
I have never hunted 50, but have several friends that do. They prefer because they can use the wide network of roads to cover a lot of country and the access in heavy snow isn't such a big penalty as in 36a. The biggest drawback is the competition from other hunters is high.
Hope that gives a little more clarity to my previous response.
Either way you will have an excellent time. It is beautiful country and makes for an amazing hunt.