It doesn't matter which you use. Both are approximately the same viscosity, light weight gear oil. That's why they are interchangeable in may applications. The difference is, the transmission fluid has some extra additives for things like your wet brakes, and anti foaming.
If you want the highest level of protection with hypoid gears use EP, (extreme pressure), designated synthetic gear oil. But, it's overkill in this application.
I have been running the synthetic 80-90w EP gear oil, in the front for 17 years.