Which would be better? Obviously for a mage zhelm all the way, but I'm curious if a 5-6 weapon attack pilgrim hat could replace a zhelm. I'm sure it depends on the job, because losing out on 20-30 dex from a zhelm might be detrimental.
Maybe if your main stat is DEX then a 35~40 zhelm could be around the same of a 5~6 pilgrim hat. but if DEX isn't your main stat then pilgrim should be better. (I haven't done any math in this so I could be wrong)
For a DrK or any class that does not depend on their secondary stat, a pilgrim hat should be better. For classes such as Hero (ST) and NL, the pilgrim hat would only be better if it was completely godly or if that NL or Hero could wear the pilgrim hat secondary stat-less. Regardless, at the very end game the pilgrim hat if scrolled well should always beat the z-helm, but it's pretty hard to reach a point where you could wear the pilgrim hat and not worry about your secondary stat.