With the enemy Fortress taken, the way into the capital is clear. Order and Destruction will both spawn into the city itself. There will be a city-wide Public Quest in a special instanced version of the metropolis. This 'contested' instance is the moment of truth for the invading army. If the defending race can throw back the attacking horde, the entire campaign - that's every zone, every keep, even the fortress - is set back to the starting position. The contested city instance is capped at 48 vs. 48 players, and the winner is chosen based on the success or failure of all instances that are in play. If the invaders complete more instanced public quests, they take the city. If the defenders complete more of the instanced public quests, they hold the line.
As the attackers, the public quest's first step will require you to kill about a hundred of the defenders. As a defender, you'll have to extinguish fires that the attackers are causing. Both sides struggle, fighting for their "version" of the city to rule. Each side, of course, has certain steps that have to be completed. As with all Public Quests, there are multiple steps to conquering the city, each more dramatic than the last. Taking control of the city within about two hours moves the city from a contested to a captured state, making the city into the ruined shadow that has appeared in so many screenshots and videos. That's when the sub-boss Public Quests fire up and the invaders have a chance to take all the marbles: the opposing side's king.
For the invaders the rewards of looting, pillaging, and burning are vast. Some of the best equipment in the game is available by progressing along the Keeps/Sieges gameplay and into the cities. There is an entire set of armor obtainable by participating in the Public Quests found in a conquered city. And, as with every Public Quest, the reward you get for participating is suited directly to you. No random drops here, with loot that may or may not fit with the individuals who took part. If you helped sack a capital city, you'll get a commensurate reward tailored specifically for your character class.