The hardness rules appear on page 272 of the CRB. They do indeed work against every type of damage equally, as you suppose: “Each time an item takes damage, reduce any damage the item takes by its Hardness. The rest of the damage reduces the item’s Hit Points.” Page 273 adds to that Object Immunities, but I don’t think they apply to your question.

If you want to homebrew this differently, please keep in mind that this affects shields as well.