In simplest terms, I believe ME3's ending was a failure for one very simple reason: it failed to evoke the emotion that BioWare
wanted it to evoke. That is not to handwave all other objections to the ending, but if you look, you can find every other complaint in a host of BioWare games. The primary cause for players to actually complain about things like plotholes (which don't really matter unless you want them to) and lack of "player choice" (there is tons of player choice in ME3,
especially the ending choice) is emotional dissatisfaction, and that is a huge problem because if the player feels unsatisfied, the past two years have shown that they will pick apart everything they possibly can to justify their dissatisfaction.
Let's introduce a hypothetical. Let's say the EC ships with the game (in all it's the-relays-are-only-disabled glory) and that the Destroy wave doesn't kill all synthetics, but only the Reapers. Do the majority care about plotholes? Do they care whether the Catalyst's logic is correct (answer: of course not, it's the villain)? Perhaps some do, but at about the same level as people cared about the Reaper baby in ME2. Sure it's stupid, but man wasn't that Suicide Mission awesome? Internet complaints are inevitable. An outcry deals in something else.
So what's this emotional dissatisfaction, and why did Dragon Age Origins, a game with ostensibly a tough ending choice, not suffer a similar fate?
There are two key components of a tough choice. The first is that the decision has weight and produces meaningful consequences (both good and bad) in the world. Otherwise we might call choosing cake over ice cream a tough choice. The second is that the consequences (both beneficial and harmful) are well-balanced between the choices. In the latter respect, ME3 is actually a resounding success, as is Dragon Age Origins. In each, there's a thought process that goes, "Well, in Ending A this happens as a result, and that's good. But then Ending A has this drawback which sucks and is absent from Ending B. But Ending B has...." and so on and so forth.
But ME3 takes condition #1 way too far in that ME3 introduces negative consequences so severe that many players feel no positive consequence can counterbalance it on an emotional level. Meanwhile, Dragon Age Origins does a good job balancing the consequences both between the choices and also within a choice. Players make sacrifices* but in each ending there is a sense that the sacrifice was well-worth what you accomplish. It's worth noting here that "balance" doesn't actually mean the negative and positive consequences are equal. This isn't even true in ME3 (the positives outweigh the negatives) and yet players still felt they hadn't achieved a true victory. It turned a bittersweet ending into a bitter or bleak ending. For the players furious with ME3's ending, it seems the positive consequences of a choice must outweigh the negative, and must do so by a SUBSTANTIAL amount. For Dragon Age Origins, the most you end up sacrificing is one life, and in all cases this is voluntary. Imagine if EDI had (through some contrived means) been able and willing to sacrifice herself to stop the Catalyst, with no other sacrifice made. That's about the level of what Origins was asking you to give.