For me, tmux has saner options and more mnemonic default keyboard shortcuts, that do not interfere with default bash shortcuts (Ctrl-A is goto-home-of-line in bash/emacs, but it is hijacked by screen by default as its escape sequence; tmux uses Ctrl-B for the same by default, which in the emacs bindings means go-back-a-character, and I do not use much, and is less likely to hit by accident).
Some of it is arguable, but for me one of the greatest benefits is how tmux will auto-resize to the smallest terminal connected, making it useful for screen sharing or when connecting to an existing session from a mobile device.