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.
don't know if there is a specific rule for this, but in this situation i would just give that stone pillar some additional resistance to slashing and piercing using the normal restance rules. maybe resistance 5, so that stabbing it is really not gonna do anything ^^
But picks are piercing, and pretty famous for being used against rocks. Maybe we should just accept that if you hit something hard enough, it doesn't matter too much what you're hitting it with
You could give it some slashing/piercing resistance. But I'd argue that is too much. Hardness 7 will make destroying the thing already pretty difficult. And unless this happens during a combat encounter/ some kind of time crunch, it really doesn't matter at all. It will just take longer. I wouldn't even let the players make the rolls, just decide it takes X minutes and move on.
@ParanoidAndroid I might do the reverse, and reduce the Hardness by a point or two for bludgeoning damage. Normally it wouldn't matter, as you say, but there will be a time factor involved. Thanks!