But... Shadow Priests and Discipline Priests have very different priorities :(
Exactly! That is why this system works. The mages/warlocks spend all of their picks on damage gear, while priests need to split their picks between damage gear and healing gear (can't let those uppity paladins get all the good stuff).
So what will end up happening is that the mages/warlocks will get the lion's share of damage gear, but priests will have priority on a few pieces, enough to treat them fairly.
Remember that the alternative is that mages/warlocks get priority on ALL damage gear, and priests get none. That's generally what happens now in priority-based loot systems. Free systems don't need to set priority rules, and wouldn't need to draft.
As an aside, I don't believe that there is such a thing as a Shadow Priest or a Discipline Priest. There is a Priest who is currently specced Shadow, and a Priest who is currently specced Discipline. People change specs, and thus need different gear for different situations. I was Retribution yesterday, and today I'm Holy. I still collected healing gear when Ret-specced, and I'll still bid on damage gear now that I'm Holy.
 5/11/35 - Extreme damage (for paladins, anyways).
 32/11/8 - I like to think of it as my Improved Seal of the Crusader build.