There's subtile difference between terminal emulators (terminator) and terminal multiplexers (tmux, screen), mentioned elsewhere [0]. IMO the main difference: With tmux, your sessions can be separate from your terminal instance. Meaning that if your terminal dies for any reason (e.g. X dying), and you've set tmux up correctly, your session will still be there and all you have to do is (re)connect.
The other reasons are probably more personal. The initial tmux learning curve is steep, but once you've got it, it rewards you with a super fast workflow that suits you. I know this sounds extremely stupid, but the "hacker cred" is large with tmux. I got hooked on tmux by a coworker who used it and ruled. I've never seen that with terminator, although it should be equally possible.
Terminator is an alternative to something like iTerm. Tmux is server based so the sessions persist after disconnecting from ssh for example and allow multiple users to connect to the same terminal
I personally would, because learning less tools is great.
I've had some problem applying this principle when using tmux locally on a system with i3. You kinda need to be consistent in which of the 2 you use to create new shell windows.
Isn't the emacs philosophy to never leave emacs? Doesn't using tmux go against that? Or do you run tmux inside of emacs?
I use spacemacs and coming from vim, its taking some getting used to but I'm still always trying to do more things in emacs and not switch to my terminal workspace.
I feel spacemacs is just a vim clone with really bad cpu and ram utilization. If I am going that road, why not use an ide like eclipse or visual studio instead?
If chrome ran within tmux, that would totally be my approach. Sadly, there remain GUI's that are better than TUI's (or rather: sadly tmux can only multiplex TUIs).