Dr Fallout
Centurion
The Brotherhood does feel more like its original incarnation, but still they seem to be somewhat off. /snip
I would say you're thinking of BoS through the lens of the West Coast too much. The one in the West was indeed a failing organization, doomed to eventually perish, but the one in the East is much stronger. They have a better idea about themselves, starting with the essential part where they actually openly recruit people. As the Midwestern chapter shows, it's absolutely crucial for survival and expansion. This one change brings more different outlooks into the fold, you no longer have just pure BoS people, but you also have outsiders who think differently and are not elitists. They, unlike the somewhat sheltered pure BoS members know what is necessary to survive out there in the wastes, they know that weapons and armor are not enough.
Thanks to this you have more personnel and more tech, as you can send out more scavenging parties. And it's heavily implied in F4 that after BoS defeated the Enclave they sort of took the area over, possibly even levying taxes from the dwellers. They could safely roam the whole area in search of useful tech too. So I'm not surprised that in those 10 years they have become so powerful. They have a better ideology than the West Coast BoS and are the biggest kid on the block in their area.
But I agree about Maxson, he is too badass for his character to be believable. Seriously, killing a deathclaw one-on-one at 12? That's a really big stretch.
Would have been better if Maxson was actually worried about his duty and made up shit to seem powerful.