Except for one thing: the Eastern BoS has no manufacturing strength to speak of. All their gear is salvaged; as per Ashur they don't actually build anything new.
That is true. If I were to try to debate this statement I'd have to consider some assumptions on how the Capital Wasteland is going to progress in the future. Which I shall since Fallout is fun. Here goes;
1. There is the Pitt; which is an incredibly valuable resource for obvious reasons. Like I said before, I'm unsure what the canonical outcome of The Pitt DLC is, but either way, it wouldn't be impossible for the Lone Wanderer to go as an envoy to Pittsburgh and convince whatever ruling power is there that 'Hey bros, there's a massive force coming in from the West, can we uh...borrow your Steel Mill? Real quick?'
If anything Ashur seems like a reasonable dude and he might be down with an alliance, even if it's temporary. Hell, he could even call up the military power of Ronto, and the geniuses of the Commonwealth, make it a party.
Alternatively the Capital Wasteland BOS could take a gamble and just try to take it the fuck over.
2. How did the NCR rediscover manufacturing? If they did it, the BOS should be able to do it as well, especially without fundamental challenges such as clean water and constant Super Mutants all up in their ass. Combined with their continual search for knowledge (the Arlington Library, for example), and its sooner rather than later.
NCR would have, if they win, the ability to turn all of their strength East. They're closing the tech gap on the stagnant Brotherhood fast. They build their own powered armor, vertibirds and energy weapons back in California, and now they're bolstered by the Archimedes system at Helios. Not only that, but they grossly outnumber the Capital Wasteland crew.
I guess this depends on what/who is lying out there in the Midwest/Great Plains/East Coast. There's a lot of ground that Fallout hasn't covered yet, and there may be a third party that's a wild card that also has the strength to give NCR a fair fight. But even if not, the NCR has to be able to expand themselves indefinitely across the entire mainland from coast to coast. One of the major things the Courier can call out on the Caeser's Legion (and thus cause them to abandon their entire efforts on the West, in just a few sentences) is this (entire conversation paraphrased as hell);
Courier: 'So uh, once you march on the West, how are you gonna babysit the East?
Legate Lanuis: 'LISTEN HERE BUDDY WE'RE THE LEGION AND WE'RE SO GREAT JUST YOU WATCH'
Courier: 'But, uh...you have finite manpower and the NCR is really, really big. So, uh...'
Legate: "'UHHH WELL YOU SUCK WE'RE LEAVING'
a massive enemy approaching you're not even aware is coming.
The East Coast BOS still has contact with the West Coast (somehow). This much is confirmed in their background story on how Lyons got dicked by his Lost Hills superiors when they changed their attitudes towards the Capital Wasteland.
I'll say this; the edge right now is with the NCR. Massively. But depending on how the East Coast plays its cards (and how the winds blow), they'll be a powerful force in its own right, very, very quickly. The days of the Capital Wasteland being a blasted hole in the ground with everyone beating rocks together, getting nothing done is over.