Compare and contrast:
The Tenth Doctor gives up Rose, with whom he is in love and has an unstated mutual romantic relationship, so that she will be happy.
The Eleventh Doctor, who is married to River Song, begs Amy to give up her husband to stay with him.
What caused the difference in the level of self-sacrifice the Doctor was willing to engage in from one incarnation to the next?
The priority of the writers is different. The showrunners approach the Doctor in different ways, and they have different ideas about what is important for the character and the show.
The Tenth Doctor was written as a person who understood consequences and dealt with them all the time. He dealt with the sacrifices he made, but mostly, the sacrifices people made for him or on his behalf. He learned that there is always a cost for his actions, and I think he tried to act in ways that did the least amount of damage.
Ten and TenToo became distinct individuals at the moment of the metacrysis, and everything TenToo experiences from that point on will be unique to him. So, Rose gets her Doctor, but the Doctor doesn’t get Rose. While we’re sad that Ten loses Rose, we don’t begrudge her her happiness. This scene isn’t written in a way that victimizes the Doctor or makes Rose look selfish. More importantly, the Doctor’s decisions will cost him and no one else; he made the choice that caused the least amount of harm.
Eleven, on the other hand, is written as a person who doesn’t understand consequences — because, he never has to face any — and who makes decisions without factoring in their ripple effect on the lives of his companions and other people he meets. Where Ten tried to leave as little a footprint as possible, Eleven never seems to consider the trail he leaves behind him; and even when he does, his tracks are always wiped clean.
Eleven is the center of the universe. His needs and desires trump everything else. We are supposed to be sad that Amy and Rory lived long, happy lives together because, they did so away from the Doctor. This scene almost blames Amy for choosing Rory — her husband — over the Doctor. This scene attempts to make a victim out of the Doctor, when nothing is being done to him. He has earned the right to be sad, but his behavior here implies that he is more important to Amy than Rory and that he deserves what he wants more than Amy and Rory deserve what they want.
In other words: Ten is man who has learned from his mistakes enough to know that acting on his own whims and desires is less important and potentially more harmful than acting for the greater good. He can make personal sacrifices because, he understands the consequences of being selfish. Eleven is a man who always gets what he wants and always “wins.” His decision to act in service of himself has never led to a permanent negative consequence, so he is completely unable to separate his wants and desires from the greater good, even when what he wants conflicts with what is right.
*I hope I worded that correctly.
Yes, this. And so many of Eleven’s story lines have to do with villains who are trying to get rid of him, whereas in Nine’s and Ten’s era the villains are usually menacing other people, and the Doctor puts himself in harm’s way to save them.