Tmux is more keyboard oriented, I guess. For example: I can copy and paste from one pane to another without touching the mouse, which is something I think is not possible with Konsole. (I haven't used Konsole or KDE for many years, so that might've changed).
Tmux is more programmable. You can write scripts to automate stuff, for example setting up a layout, etc. with a degree of freedom that is not possible with Konsole.
You are probably fine with your setup, not trying to convince you ;-)
Personally: I just like fancy TUIs. One of the first things I programmed was mIRC scripts, might be because of that.
Just a suggestion, it's easy to capture command or program output with xsel, just by piping into it, for e.g.: 'ls | grep -i "whatever" | xsel -b'.
It is common for me and I have aliases set up for 'ls=ls -lah', g=grep -i' and 'x=xsel -b', so the actual commandline looks like 'ls | g "whatever" | x'. Then I can paste or redirect the result into something else.
There are probably better command line clipboard managers, but I just happened to settle on xsel, and it seems to work pretty well. That, and using alt and number keys to switch between tabs gets me pretty far with my terminal emulator.
Tmux is more programmable. You can write scripts to automate stuff, for example setting up a layout, etc. with a degree of freedom that is not possible with Konsole.
You are probably fine with your setup, not trying to convince you ;-)
Personally: I just like fancy TUIs. One of the first things I programmed was mIRC scripts, might be because of that.