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Per the Initiative rules in Combat, when multiple characters have the same initiative, the one with the higher initiative modifier goes first. If they have the same Initiative modifier, then the rules say roll to see who goes first.
Pair this with the basic rule (as I understand it) that you determine initiative at the beginning of combat and it does not change during combat, except pursuant to the Special Initiative Actions (Delay & Ready) and perhaps certain spells/abilities which specifically say they cause a change in initiative.
In most game play I've seen, the GM allows people with the same initiative to elect to let others go first within the same initiative count. This should be ok as a form of the Delay action and in any case I don't see a problem with it. BUT, that requires conscious cooperation. When one person is sleeping, they can't take actions, so can't elect to Delay their action.
Thus, in your specific situation, if your GM followed the above, your GM should roll to determine which Duergar goes first. If the sleeping one goes first, then he loses his action (as he awakens after his initiative count and needs to wait until his next initiative count to act again). If the awake one goes first, then the sleeping Duergar gets to act because his initiative comes after the one who woke him up. In either case, the now awake the Duergar gets his full action... the question is when does he get his full action.
This assumes you accept that sleeping/helpless characters cannot take actions. The helpless definition in the glossary doesn't specifically say so and I'm sure that there are one or more people who would argue that you can take actions when sleeping because it doesn't say you can't. If you accept such arguments, then I guess the sleeping Duergar could Delay its action to go after the other one wakes it up.
There are other ways to analyze this, such as saying that the sleeping/helpless Duergar has a -5 DEX, which reduces his Initiative modifier by 2, this giving him a lower initiative modifier for the purposes of breaking a tie, so the awake Duergar goes first. Implicit in this is that the change in Initiative modifier does not actually change the sleeping Duergar's Initiative count, just his Initiative modifier (which is used to break ties).
Bottom line is I'd defer to the GM, BUT a good GM should probably explain how he's doing this and be consistent in his future rules. The GM shouldn't bounce around between different ways of doing this as it can make PCs feel as though they're being picked on, especially if it results in good results for NPCs, but (in the same situation) bad results for the PCs.
