the brains thing comes from something Klopp said himself ages ago in an interivew, and it got picked up on. He said that Zeljko was the brains of the team and Peter Krawietz was the eyes of the team. I kinda saw it as typical Klopp downplaying his role in a way, something he's done a lot, he loves giving his assistants credit.
But Buvac is an outstanding coach. I think the deal is, is that of course both he and Klopp have very much the same ideas about football and how it should be played, but Buvac is the one who transfers their ideas onto the pitch. He is like the academic of the pair, the one who puts it on paper and then onto the pitch. He's the one in the training sessions who will actually place players where they need to be to carry out their patterns of play.
It would remain to be seen how either does without the other I would say. As they've not worked a lot apart. Buvac did work as a head coach for a while, but at lower league level in Germany before going back to Mainz to be assistant coach to Klopp.
I honestly have no idea if he would make the step up into the limelight well. But he is a superb coach, he is like a football encyclopedia.