Brotherhood is an official anime. SAO abridged is a fan made parody on YouTube. it recuts and redubs but that’s it. And its purpose isn’t to tell the whole SAO story, it’s to make gags. It just inadvertently made a better story than SAO itself, mostly by changing certain characters motivations

Edit: oh and if you’re intent on watching the full version at all, watch it before the abridged

Mine is legitimately just watch SAO abridged. It reworks story beats for a smoother story in addition to adding gags