In my opinion, maybe some of the confusion here is that your example does not fit well.
"In future" and "from now on" have pretty much the same meaning, in my opinion, so you are right about that. Also, as you say in your comment "in the future" has a distinct meaning.
However, the example about people living on the moon is more likely to go with "in the future" rather than "in future/from now on". That is really do with immediate future and therefore unlikely to apply to something as speculative or as general as living on the moon.
I don't know if this helps or not.
My answer to your initial question would be "equally likely to be used, neither is more formal than the other".