None of these abilities "activate", they trigger. In particular, Hidden Stockpile only triggers if a permanent you controlled left the battlefield this turn. Obzedat, Ghost Council exiling itself in the end step won't happen in time to meet this condition. This is due to what's called an intervening if clause. If no permanent you controlled left the battlefield this turn, only Obzedat will trigger.
603.4. A triggered ability may read “When/Whenever/At [trigger event], if [condition], [effect].” When the trigger event occurs, the ability checks whether the stated condition is true. The ability triggers only if it is; otherwise it does nothing. (...)
Assuming another permanent did leave the battlefield, both abilities trigger at the same time - at the beginning of the end step. Since you control both abilities, you choose the order in which they are put on the stack.
603.3b. If multiple abilities have triggered since the last time a player received priority, each player (...) puts triggered abilities he or she controls on the stack in any order he or she chooses. (...)