As for an all out war, not just wich i prefer, Id have to say the West Coast would win. Due to their much larger bank of pre-war tech compared to the East.
No, they would not. Tactics and hardware don't mean jack if logistics are insufficient. The East coasters' home base is the Citadel. The west coasters' home base is thousands of miles away. That's a looooong way to travel.
The East Coast have their own tech, even better than pre-war: fresh spoils of victory from their Enclave entanglement, don't discount that. That includes plasma rifles, salvaged enclave power armor models, and vertibirds, as well as an air field to operate them out of.
Besides... the Outcasts no longer have a leg to stand on now with harping on Lyons for not doing tech recovery. Lyons has a heaping pile of aforementioned Enclave spoils, as well as a high-volume water purifier. So now the Outcasts are stuck holding the Deserter bag. The West Coasters will not be happy with that. Desertion is a serious offense.
And finally, Lyons is in the right. One of the definitions of "Technology" is "application of science". What good is technology if it's just squirreled away?