I'm thinking of this line from Dean: “And when Satan takes you over, there's got to be somebody there to fight him, and it ain't gonna be that kid. So, it's got to be me.”
It’s classic Dean, classic Winchester: a sacrifice for somebody else. Dean describes it as a simple inevitability. Dean is more....resigned than Sam. We see this again and again. When Cas becomes Godstiel, Dean wants to drink alcohol and watch porn (Or, as Dean says later that season, “It's called anime, and it's an art form.” I can't tell you how much I love that line.). We see is as far back as Croatoan: Faced with Sam's death, Dean gives up. He won’t let anyone kill his brother, but instead he chooses to die with his brother against his brother’s wishes. He’s worn out by hunting. Dean seems to get emotionally worn out like this more easily than Sam. Sam quit hunting when he went to Stanford, but he wasn’t tired. He just hated the instability, the constant fear. And he decided to do something about it. As I've said in previous posts, he's action boy.
Dean choosing to “yes” to Michael in PoNR is a bit passive. Dean has decided that it is inevitable that Sam will say yes. And Dean can’t let Adam get hurt because that’s not what Winchesters do, so it has to be him. It’s also a symptom of Dean’s own brand of self-loathing. It’s similar but different from Sam’s willingness to accomplish things at all cost - including any cost to himself. To Dean, everything is his responsibility (remember, Mary, John, Jess, Ellen, and Jo are all people Sam and Dean have "gotten killed"). The best solution is usually the one that requires incredible self-sacrifice on his part, and is (in his eyes) the best-of-a-bunch-of-lousy-options solution that causes grief to others as well as Dean himself. While Dean is more focused on the sacrifice, something that will merely lessen a disaster rather than stave it off, Sam is more focused on a positive goal. Sam will burn himself out for a goal, but he won't lose sight of the goal. Sam doesn't generally despair - when he hits a wall, he switches goals. Sam is stubborn.
The two of them go to extremes at times. Dean jumps to fatalism when there are other options, and has been known to make choices based on indulging his self-hatred rather than on what is actually best. He also has a tendency to confuse his self-loathing with righteousness, seeing himself as man whose goodness has been corrupted, and who can therefore take the hard but necessary actions that others are not strong enough to see.
Sam can become tunnel-visioned in pursuit of a goal, dismissing side consequences of his actions, not seeing when he's being played. He can also be so eager to DO something that he doesn't know when to stop, when to let it be. Sam is good at learning from his mistakes, but the one mistake he doesn't learn from is the mistake of thinking that you should and can always learn from your mistakes.
Dean saying “yes” to Michael is giving up - Sam saying “yes” to Lucifer is getting shit done.