Brotherhood-Enclave War

The Capital Wasteland BOS-Enclave War was a military conflict in 2277 between the Brotherhood of Steel and The Enclave.

Prelude
When the Brotherhood arrived in the Columbia Commonwealth area in 2255, they did not yet know that the Enclave, who were defeated by the California chapter of the Brotherhood and the New California Republic sixteen years ago, had fled to the Columbia Commonwealth. Under the leadership of Owyn Lyons the Brotherhood began combating the local super mutants, unaware of the rebuilding Enclave.

War
In 2257, the Enclave commenced a propaganda campaign against the Brotherhood. The Enclave, now under the leadership of president John Henry Eden, plotted in secret at Raven Rock. For twenty years, there was no interaction between the two factions, leading many to suspect the Enclave radio broadcasts were on an old loop. However, in 2277, Colonel Augustus Autumn led an attack on the Jefferson Memorial, and took over Project Purity, as part of their plan to "purify" the wasteland. James was among those killed, and the Lone Wanderer and the other survivors escaped to The Citadel.

The Brotherhood Outcasts were also attacked by the Enclave on patrols. Occasionally, the Outcasts would also launch attack against Enclave, but they were not very organized. Protector Henry Casdin largely left the Outcasts out of the war.

After the Jefferson Incident, the Enclave began their conquest of the Columbia Commonwealth, establishing many small camps & outposts throughout the capital wasteland. They even tried to annex Vault 101, but were denied entry by its isolationist overseer.

The Brotherhood began to try and get evidence that Project Purity could restart so they could reclaim the Memorial. The Enclave got wind of this, and kidnapped the Lone Wanderer in Vault 87, confiscating the G.E.C.K.. The Lone Wanderer awoke in captivity inside the Enclave base Raven Rock, being interrogated by Colonel Autumn. President Eden soon summoned The Lone Wanderer to his office, where he was revealed to be a ZAX computer. President Eden recruited the Lone Wanderer to act on his behalf and gave them a vial of Modified FEV, then facilitated their escape from Raven Rock.

After the Brotherhood received word that the Enclave possessed the means to activate the purifier, they launched an operation to reclaim the Memorial with the support of Liberty Prime. The Brotherhood forces and the Lone Wanderer stormed the memorial and defeated Colonel Autumn, then started the purifier. Two weeks later, the Brotherhood dispensed the water throughout the wasteland. The Enclave, after it's defeat, made a last stand at Adams Air Force Base. When the Brotherhood invaded their satellite station, the base was destroyed, but Liberty Prime was eliminated, a major blow for the Brotherhood. After creating the Tesla cannon, they launched a final attack on Adams AFB. The Enclave stood a last defense, but were defeated by the Brotherhood. As a last resort, Whitley, a scientist, launched his prototype eyebot, ED-E, to go to Navarro and complete a mission. The mission is unknown.

Looking at the launch terminal, it appears they were planning to eradicate the settlements of Megaton and Rivet City. They also had Project Purity, and the Citadel as targets. You can target the Citadel if you want and completely destroy the Brotherhood, or target Adams and conquer the Enclave. Neither option has been confirmed as canon.

Outcome
If the Brotherhood won they would still continue to have problems with the Enclave as despite the destruction of Adams Air Force Base remnants of the Enclave will continue to roam the wasteland, but will not pose as great of threat as before and have no known goal. If the Citadel was targeted the Brotherhood would be destroyed and with it's leader dead and most probably Lyons Pride being dead they would have no clear goal. Their future would be uncertain.