Barkov is better right now. Matthews is more of a force offensively, but the gap isn’t nearly as big as the advantage Barkov has over him defensively.
That could change as early as this coming season as we will hopefully see a full year of healthy AM. He managed just over a PPG last season but was injured for a number of the games he did play. His goal apparently is to be the best two way C in the league, but we will see.
Either way, we are comparing two of the best young centres in the game. Barkov will probably always be a bit underrated by the media while Matthews may get the opposite.