There seems to be a correlation between perception, (and GP? I'm not sure on this one however) and HQ items. While it's not certain, I tried gearing my Botanist with the perception items (she now has the full level 60 set) and melded everything with perception. She now has 610 gathering, 639 perception, and while earlier I barely saw any HQ items (gathering did increase the number of items she could get, however, it's all 20 or 30 now), she now occasionally brings me back batches of 20 hq dark chestnuts (sometimes there's a split, like 17 nq 3 hq, but full hq batches seem common). My two fishers seemed to have a difference in the ability to bring back hq items based on their gear, too.
So in short:
Gathering: ability to gather items, amount of items (caps)
Perception: ability to gather hq items, amount of hq items (randomized)
GP: ???
Level difference: time for venture completion (10-19 level difference shaves 10 minutes,20+ level difference shaves 20 minutes, and it caps there)