I'd assume the one you have equipped.
Keep in mind I don't have the attack level to equip the rune one.
If this isn't just a hypothetical question, why not unequip and bank the iron one? Problem solved.
Just take a close look at the color of the hatchet that you're using(the one that's actually doing the chopping). If it's a gray you're using iron, if it's more of a teal it's rune.

