Continuing from last strip's comments:
Presenting a quest to the PCs as an out-of-character GM narration has the advantage that the players know exactly what the quest is, and can start the several hours of prepping and choosing equipment from the equipment lists right away.
Presenting it to them in-character as an NPC has the advantage that the PCs can argue about whether or not they should accept the quest, or in fact what the quest actually is, or they can even reject the quest outright.
This latter option, rejecting the quest, is actually an important part of The Hero's Journey, as outlined by comparative mythologist Joseph Campbell in his seminal book The Hero with a Thousand Faces. The first stage of the Hero's Journey is the Call to Adventure, which is followed immediately by Refusal of the Call. We see this in Episode IV: A New Hope, when Luke first learns of his father from Obi-Wan, and of Obi-Wan's request to follow him on a quest to rescue Princess Leia. Luke's immediate reaction is the Refusal of the Call:
Alderaan? I'm not going to Alderaan. I've got to go home. It's late, I'm in for it as it is. [...] I can't get involved! I've got work to do! It's not that I like the Empire. I hate it! But there's nothing I can do about it right now. It's such a long way from here.
Similarly, both Bilbo and Frodo initially reject the respective quests offered to them by Gandalf, and there are dozens of other examples going back all the way to Greek and Babylonian mythology. So if you wish to mine this rich vein of heroic archetypes, you have to allow your players the option of refusing the quest. Of course later* you drag them into it anyway since you've spent over 100 hours writing the damn adventure, but you have to give them that chance.
* Sometimes years later, after they're finally done with that thing they decided they wanted to do instead that you then had to make up on the spot.
R2-D2: Finding some kids' lost parents? Boring hook, but it could lead to something interesting.
Luke: I know! We'll ask Yoda. His midi-chlorians should be able to search a huge area in no time.
GM: Um... You call for Yoda, but he's not there.
Luke: What? That's odd.
Chewbacca: Clearly something's happened to him.
R2-D2: Aha! We've already found the real quest!
C-3PO: He can't just fly through space. Someone must have taken him away.
Luke: Quick! Who's left Endor recently?
Wicket: Um... Wedge left yesterday. He said he had a mission.
R2-D2: The game is afoot!
Wicket: Er... What about the kids with the missing parents?
Luke: Just feed them some... native boar-wolf or something until we get back.
Wicket: But how will they pay for it?