Back on topic.

I have no idea which aircraft Korean Air uses on HAN-ICN v.v., so you will have to double check on that to see if an old aircraft will be involved.

If it's only $75, Korean Air wins over China Airlines in every aspect except for the transit time. However, I am sure ICN is considerably more interesting than TPE for your kids.

One thing to note is, I remember Korean Air has two kinds of lounges in ICN. One is fantastic and the other is normal. I am not too sure which lounge you will get cause you are indeed taking their flight but not having status with them.