Minimal difference for rust, as everything is done through the Unity Player, and nothing except invoking the plugin happens through firefox'es plugin layer. Plus nightly has both stability and performance improvements, is updated more frequently, and has a heck of a lot more time and and developers riding on it compared to Palemoon or Waterfox.
Good to know but I have found water fox project to be smoother ingame then nightly, but yes nightly is updated more frequently as it is just the most current dev iteration of Firefox not sure if its necessarily more stable though. swapping from nightly to waterfox got rid of the choppiness when turning around quickly for me. Client will be out soon though and we won't have to use either thankfully. I recommended Waterfox as its meant for running these type of things also has some useful troubleshooting tools built in on crashes. Also because I was confused at the nightly is just Firefox for 64 bit computers as that is not what nightly even is.
EDIT: Seems with Alpha keys not being sold, transition will be incoming very soon I feel now, so if you don't feel like installing our browser recommendations just wait, shan't be long I'd imagine.