I think it's telling that the Paladin paint scheme on the Maxson BoS's armor looks more like the Outcast's schema than the Lyons branch's schema. I've been positing for some time that to influence the Outcasts in returning, Maxson had to give them leadership positions, which explains the influence they've had on the organization (and the change in color schemes - knights look similar to the old Lyons BoS scheme, but Paladins and Sentinels are distinctly Outcast in appearance).
Examples:
http://vignette2.wikia.nocookie.net/fallout/images/0/06/Outcast_Patrol_2.jpg
https://assets.vg247.com/current//2015/11/fallout4_guide_paladin_danse.jpg
http://vignette4.wikia.nocookie.net/fallout/images/f/fc/Lyons_Pride.jpg
http://fallout4.wiki.fextralife.com/file/view/T-60_BOS_Knight_Paint.jpg/568382675/T-60_BOS_Knight_Paint.jpg
What this tells me is that the Outcasts ended up with major influence in the new organization, enough so that their color schemes were adopted for leadership positions, whereas the old Lyons colors are only seen (and not even as the major color, but as an accent) on the Knight (read: rank and file) members T-60 frames. This also explains the 'backsliding' that's so apparent in turning more towards their focus on forbidden technology in comparison to the focus the organization had in Fallout 3 (which is why the Outcasts left in the first place).
Maxson is in charge, but it's the Outcasts who changed the Brotherhood, not the other way around. I would say that Henry Casdin's rebellion was a complete success in accomplishing what it set out to do... revert the BoS back towards the old ways. It wasn't 100%, as there's still some desire to defend those who can't defend themselves visible in the Brotherhood, but the organization resembles more of what Casdin's troops did in Fallout 3 than what Lyons' soldiers did.
The male Sole Survivor, when speaking to Danse as an Initiate, can mention his previous military service when Danse is explaining that he expects military discipline from the Sole Survivor. Danse proceeds to state that he'll cut the explanation about discipline short as he expects the Sole Survivor to know how to follow orders.
It's really easy to see how the BoS would be comforting to a veteran. They fight similarly to the US Army pre-war (power armored elite troops backed by infantry in combat armor with vertibird support), have a structured organization (even if the rank names have changed from things like Sergeant, Lieutenant, etc), and it would replace an alien environment with one very familiar -- barracks, soldier's comraderie, etc.
The Brotherhood make perfect sense as a faction choice for that very reason. Not that others don't as well, I am merely stating I understand the choice being made. Destroy the thing that took your son, live in an environment that you're familiar and comfortable with once again after possibly months in the wasteland, and then fight back against the "unnatural" things that have overrun your home and country (synths, supermutants, raiders, ferals). I can imagine the allure is very, very strong (especially to the male, war veteran survivor).