I'm sure there are some advantages, but I couldn't quickly figure out how to get it running with the various jump hosts required (and I also often use port forwarding...). Just having tmux on the other side gets me most of the advantages, I think...
Well, on port fwd, maybe if you forward the mosh server port would work. If you use SSH itself as a tunnel, the setup it's far complex, as mosh is just a remote shell.
Still, mosh curb-stomps ssh on latency, input guesssing, data saving and bandwith usage.
Using that over 2G was a literal black/white difference compared to SSH which was nearly impossible to connect and the latency was unbearable. Under mosh I could chat, email, nntp (they still are some good newsgroups), IM over jabber/telegram, read news over RSS, code in C/TCL (jimsh) and read the docs with links, among reading books (novels and essays) with some CLI epub reading script.
Yes, I also used tmux on the remote machine too, mosh+tmux work great with each other. Albeit mosh resumes a potentially lost/dropped connection just fine (even without a running remote tmux/screen), I think tmux itself would send less data over the wire.
