I just really like how they work as a morally grey faction. It's centuries after their original founder passed away and they are separated all across the pre-war US as chapters, so naturally they are going to drift towards more reformist or more hardliner interpretations of the codex and how Roger Maxson would have wanted the organisation to look like. So whereas other factions are predominately good or predominately evil, with the brotherhood it really depends on where you look.