I am a huge fan of the original Fallout games but I will have to say that I like the East Coast Brotherhood a lot better. By the time of Fallout 2, the BOS was almost completely obsolete as they are no longer the largest or even the most technologically advance faction around. They were desperate enough to start a full scale invasion of the NCR in hopes of taking away technology from the hands of 'inferior people'. At this stage they are almost just as bad and evil as the Enclave.
The East Coast BOS on the other hand actually set out to help rebuild civilization and help the common wastelanders. Playing the role of an NCR for the East. They might be in bad shape right now, but in the long run they will last a lot longer then the original Brotherhood.
In terms of recruiting ability: East coast BoS has manpower to it's advantage. They recruit just about everyone.
In terms of experience: East coast BoS has been fighting a war against not only the DC mutants but also against the Enclave. EBoS was outnumbered by the mutants 500:1 (easily) and outnumbered, out-gunned and still managed to win that war (With the Wanderers help)
In terms of technology and firepower: Liberty prime and the ruins of Adams air force base (as well as the ruins of Raven Rock, which anyone could gain access to with time and heavy equipment)
In terms of personnel: The EBoS has traveled across the hostile ruins of the former United States gaining goodwill and personnel.
Science: BoS has access to the same scientists who managed to bring back Liberty Prime. No small feat.
Terrain advantage: EBoS also has the terrain advantage. The Eastern Brotherhood knows the DC area in and out.
Goodwill: Eastern BoS also has the goodwill of most of the population due to not only bringing back a pre war water network but also by a policy of helping the local population with supplies, manpower,knowhow and life giving water.
In terms of supply lines: Eastern BoS would have a lot easier time of resupplying and restocking. The Western BoS would have to fight a war across a whole bloody continent.
Command and Control: The Eastern BoS (assuming the continued existence of the Citadel) has a command center to quickly coordinate attack and defense and virtual instant communication with troops in the Field. Western BoS is moribund, slow moving and hierarchical. It could be days or even weeks between communication between whats left of the Western Command and any invasion force.
And I am not even going to speculate what conducting a two front war would do to the Western BoS. I am speaking logistically. NCR and Eastern BoS at once. Any invasion efforts, would be like Germany's war with Britain and the USSR. NCR being the USSR and EBoS being Britain.
And last but not least: Eastern BoS (assuming a lot here) also has the support of the Lone Wanderer and vault messiah.
It wouldn't even be a fight it would be a hands down one sided slapdown
The only way that the WBoS would be able to destroy the EBoS is if they landed under a flag of friendship and captured the Citadel. Even then though, I think that plenty of BoS people in the field would launch a counterattack (with plenty of local support) within a short time.
The only way that the EBoS would be able to short term make a war work would be by flying into the Citadel, blowing it sky high then working to eradicate all of the well trained, well armed and very angry BoS in the surrounding area.
Finally think about this: The highly trained, highly motivated Eastern brothers have been fighting a two front war, outnumbered, out gunned, against not one but TWO numerically superior enemies, and are coming into this conflict having lots of experience doing this without so much as a peep from anything approaching a command structure for YEARS. Even assuming that the WBoS manages to take and hold the Citadel (or blow it up). Optimistically speaking, even if everything goes RIGHT for the WBoS and they manage to wipe out and or capture everyone at the Citadel, and recruit the outcasts to do their horrible and dishonest dirty work, it would be a knock down, drag out and likely LONG war to reassert command of the area.