This. Clicking? No. Alt+Shift+Number? No. Good old-fashioned Ctrl-a ".
Command-left, command-right.
What are the main advantages of screen/tmux in comparison with simple terminal tabs?
For starters, detaching.
Mainly the detach/attach facility. I can open it from ssh, without even closing the session in the terminal. They also provide split window facilities, tmux even more so.
My tabs and state are on the REMOTE end of my connection. I never lose it.