We won't ruin all the fun for players, but the following definitely contains major spoilers for the ending of Mass Effect 3.
From the outset, the "assault on the beam" in London has been modified to make more sense of Shepard's squad members being seen alive later. Shepard calls in the Normandy to take both squad members away after one is injured in the assault. Depending on your squad's configuration, you might get an added final "no matter what happens, I love you" piece of dialogue between Shepard and his love interest, which is the right moment to have a box of tissues nearby.
Nothing appears to change in the next few scenes, at least not outright. Shepard still has a few husks and Marauder Shields to blast through before diving into the beam that takes him to the Citadel. At this point, BioWare added scenes that show more of the battle in space, with a Reaper that sort of "grabs" an entire Alliance ship. In the midst of the chaos, the Crucible is seen flying in with Alliance support, where Admiral Hackett receives a report that "someone made it to the beam," which seems to explain how Hackett got back in contact with Shepard and knew he was on the Citadel.
Shepard is clearly seen flying through the air and landing hard in the corpse-ridden Citadel tunnel now, and the pistol he was carrying is nearby. In the original ending, he only wakes up in the mess in a daze and seems to "find" the pistol he uses to shoot Anderson. Not much seems to change in the exchange between Shepard, Anderson, and the Illusive Man, making the final confrontation with the Illusive Man one of the main constants between the original and revised endings of the game.
Shepard still speaks with the Catalyst, the boy that fans refer to as the "star child." In the moments leading up to the commander's final decision, three primary dialogue options have been added in which the Catalyst elaborates on questions players have been asking since the game first launched months ago. The Catalyst explains to Shepard that it's essentially an A.I. constructed to bring balance between organics and synthetics, and elaborates on the purpose of the Reapers and the Crucible. We won't spoil the juicy stuff here, as your Commander Shepard should hear it for himself.
What hasn't changed is that Shepard still has a pretty big decision to make. The same three options in creating a new "solution" are in play, but in the Extended Cut version the Catalyst explains in greater detail just what will happen if Shepard chooses any of those routes. New this time around is the ultimate renegade choice, in which players can throw out the Catalyst's "three options" scenario and let the fighting continue, which results in disaster for the current cycle of civilization and a scene in which Liara's data capsule is seen telling the tale of humanity's failures on an unknown planet.
Choosing any path nets players a more fleshed-out ending than before. Troops of different races (depending on whether they were spared based on the kindness of Commander Shepard) are seen fighting and celebrating on Earth. A sequence was inserted in which Joker is ordered to withdraw the Normandy and zip away from one of the major criticisms of the original ending. Most noteworthy are the final sequences, in which the Normandy crew stands around the ship's memorial wall, where they place Commander Shepard's name above Captain Anderson's as a final "goodbye" to the game's hero (though, yes, one of the endings still hints at Shepard living through the catastrophe).
A more jarring addition is the epilogue near the very end of the Extended Cut DLC. Depending on which of the three choices Shepard makes (this scene isn't used in the new fourth ending of the game), a different narrator (Shepard, Hackett or EDI) will briefly put the commander's decisions in a sort of "universal" perspective, fleshing out the immediate future of the species in the cycle.
Each narration differs between the three endings, and is paired with both standard cutscenes and an artwork slideshow. It's an unusual addition, but does add more weight to each of the three options, on top of a hefty amount of explanation. It certainly makes each option feel more different from one another. In one piece of artwork during the middle option known as "synthesis," players even get a small glimpse at the face of a Quarian.
Some changes in the Extended Cut version are subtle, but they also strip away some of the mystique of the original ending. They affect, but don't destroy fan theories surrounding the original ending and add more definition to some of the more mysterious elements of the game. In some ways, the Extended Cut DLC answers burning questions while maintaining a little wiggle room for fans to speculate.