mosh by default doesn't support native scrollback. The way mosh is implemented (by default at least) is to just paint the screen locally with the remote "view".
If you try to scroll back in your terminal locally (literally scroll up with a mouse/trackpad), it will scroll up your local terminal instead of scrolling up in the remote view. So your scrollback is literally capped at the vertical height of your local terminal window.
This is super annoying if you want to see long output of a previous command or even see what the output was of the command you ran five minutes ago.
ET solves this by basically doing ssh under the hood. So you have real scrollback by default. It's REALLY nice and is one of the primary reasons I use ET.
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As far as tmux control mode, in essence, it allows you to control tmux via your native terminal commands. On iTerm for example, you can use the key command to vertically split the (iTerm) terminal and tmux will actually hijack that command it do it in tmux. So you can use your native terminal multiplexing commands instead of the tmux key commands.
I only know of iTerm 2 that supports this functionality, just as a heads up.
Not being able to scroll was a pain, but nothing that tmux or even output piped to less couldn't solve. It wasn't glorious, but it worked. That said, might be tempted to try ET just because scrolling through long winded outputs are a frequent thing.
Smooth-scrolling back through a command that unexpectedly dumped 500 lines of output, using Alacritty and a big scrolling trackball with acceleration, is pretty glorious.
If you try to scroll back in your terminal locally (literally scroll up with a mouse/trackpad), it will scroll up your local terminal instead of scrolling up in the remote view. So your scrollback is literally capped at the vertical height of your local terminal window.
This is super annoying if you want to see long output of a previous command or even see what the output was of the command you ran five minutes ago.
ET solves this by basically doing ssh under the hood. So you have real scrollback by default. It's REALLY nice and is one of the primary reasons I use ET.
---
As far as tmux control mode, in essence, it allows you to control tmux via your native terminal commands. On iTerm for example, you can use the key command to vertically split the (iTerm) terminal and tmux will actually hijack that command it do it in tmux. So you can use your native terminal multiplexing commands instead of the tmux key commands.
I only know of iTerm 2 that supports this functionality, just as a heads up.