I killed him and the only thing I'm salty about is having the quest stuck in my inventory, lol. In retrospect I should have let him live, to be honest. My logic was that I needed the crown for the main quest (INT boost), but I needed the axe to survive the Ark (and in general I also wanted a better weapon ASAP), and I couldn't have both of them at the same time since getting the axe would mean no crown, keeping the crown would mean no axe. So I killed him. But I only killed him after getting the ring from the minotaur seer or whatever she is. And then I killed her too, and got a really nice necklace for Hirge.
Short-term it was great, crown did what it was supposed to do, necklace worked great with Hirge, axe really helped out in the Ark especially since that damn maul didn't drop until the very end (as if to spite me, lol). Long-term though, it's not that good given how I now have a crown I don't need and a cloak I don't need, a better necklace for Hirge rewarded at the end of the main quest, and a quest in my journal that I can't complete. I guess Grissenda can have the cloak, and a future mage companion the crown. So yeah, sitting right now in my position I can say that "gee I wish I hadn't killed that goddamn king", but honestly, the rewards I got right there and then for killing him probably made my next 10 hours and most of the Ark much easier.
In the end it boils down to a choice. If you actually need the cloak and the crown even after the main quest then I'd say just kill him. If you don't think you do, then it's up to you whether or not you want to have an axe now or later.