Instead of figuring out how to make the hard choice between Urgent<->Important in the first place, you've drawn a distinction which lets you kick the can down the road.
Choosing between Unurgent-Important<->Urgent-Unimportant is exactly the same problem as choosing between Urgent<->Important.
You have two tasks: A or B. Which one should you work on first?
The one which is most important/urgent/crucial/paramount/valuable/critical/indispensable/pressing/essential/serious/vital/exigent/burning/paramount/<insert more synonyms here>, obviously!
Is that task A or task B?
"The first principle is that you must not fool yourself and you are the easiest person to fool." - Richard P. Feynman
If you can't assign relative priorities to things - you can't implement a priority queue ( https://en.wikipedia.org/wiki/Priority_queue ).