I'm still running Out of the Abyss, and we're currently half way through Chapter 9: Mantol-Derith. The party is level 9 now (awarded as we transitioned between Chapter 8 and Chapter 9).
As we started Chapter 6: Blingdenstone, we decided to start using milestone levelling rather than tracking XP as we had been doing up until that point (DMG, pg. 261):
Level Advancement without XP
You can do away with experience points entirely and control the rate of character advancement. Advance characters based on how many sessions they play, or when they accomplish significant story goals in the campaign. In either case, you tell the players when their characters gain a level.
This method of level advancement can be particularly helpful if your campaign doesn't include much combat, or includes so much combat that tracking XP becomes tiresome.
This last point about tracking XP becoming tiresome is pretty much why I suggested the switch to this method. It's worked well so far, since interesting significant story moments have made it feel well paced, and there have been enough random encounters as we travel between locations in the Underdark (in addition to the "story combat") that the levels feel earned.
However, planning ahead, I want to make sure that the levels are awarded at the right pace so that it doesn't feel rushed, but at the same time making sure that enough has happened so that it continues to feel earned. Personally, I don't feel like enough is happening in Mantol-Derith to justify jumping up to level 10 at the end of that chapter, for example.
Also, although the players like roleplaying and love meeting the various characters of this adventure, they're not too interested in the factions like the Harpers and all that, so they were kinda glossed over during Chapter 8, so although roleplaying experience can still contribute to these levels feeling earned, I can't just have huge lengthy faction arguments to justify it because my players won't really engage with that.
The PCs should be level 15 for the last chapter of the adventure, as suggested by OotA, pg. 217, which implies such by saying:
Confronting the Demon Lords. The demon lords are some of the most powerful foes a party or adventurers could face. Indeed, any one or them at full strength could wipe out a group of 15th-level characters with ease.
As well as being more explicit about it on pg. 143:
Ideally, the characters should be 14th level by the time they crash Zuggtmoy's wedding (chapter 16, "The Fetid Wedding"), and 15th level for the final showdown against the demon lords (see chapter 17, "Against the Demon Lords").
So, level 15 by Chapter 17, and before that, level 14 by Chapter 16. However, I can't find anything more explicit about the levels in between, which means it's up to me to judge that.
So, currently they are level 9 as we play Chapter 9, and they've got to reach level 14 by Chapter 16. There are more remaining chapters here than levels, so simply handing out a level at the end of each chapter won't work.
I am hoping that this will still fall under the heading of "Good Subjective" if I word it in this way: For those who have experience running/playing in OotA, what levels were the party during each chapter or significant story moment during these chapters (10-15)?
Just to re-iterate, if you don't have experience running or playing this adventure, don't answer, since inevitability such answers can only be speculation (hopefully this question won't end up on the HNQ like my last one, which is where those sorts of answers usually come from...)