I am currently porting a Ruby application over to JRuby, and use tmux (although I am pretty sure screen would behave the same). Let's say you have two rubies installed, ree and jruby. You start out using ree, and are using screen/tmux, and have two screens open.
If you switch to JRuby in the first screen, then switch to the second, the changes don't propagate. e.g.:
It's not a big deal -- you just have to make sure you do the right thing -- but it is unexpected and has burned me a couple of times. It looks like rbenv won't suffer from this problem.
Of course that is expected behaviour: tux loads multiple independant shell environments. A change in one will not affect the other. The same holds true for modifying the PATH environment variable, which is how rbenv works. So I'm not sure how you're expecting rbenv to avoid that behaviour.
But thats exactly, what I expect from rvm. When i'm in in one projecti want too to use that Ruby with that gelder and not the other Ruby and gemset. So rbvm is not want I want to use with tmux.