recently i started 2 new game on KH1.5: the first one is pround mode lv1 and the other is beginner mode (wanted to do one without doing the playrun and wanted starting a new game just so)
anyway the fact is in the first one is hard find a single potion, meanwhile in the other i find more potion and other object.... so the difficult can be on some influence about the drop rate or is just pure coincidence? :/
PS: counting in both games i haven't the skill that increase the item's drop rate. :D

As far as I remember, in Proud Mode it's harder to farm items, that's why I always go for the shield and give up the sword to get Lucky Strike fast