Basically Oates coached all the Caps to play hockey like Adam Oates - putting a premium on read and react. As a player, few were better than Oates at reading the play.
But the reason why Adam Oates was a special player was that most hockey players don't have that as their primary skill tool - so a guy that is highly adept at reading and reacting becomes a unique asset when playing with guys who on the ice who are mostly initiators - whether through speed, physicality, puck-handling, tenacity, shot, etc.
But a team of Adam Oateses, is a team of passive, read-reactors. You have to have guys on the ice being aggressive and taking the play to the other team, otherwise you're on your heels the whole time and you're never in control of the game - the tempo is dictated to you, instead of by you.
Oates, as we all know, never tried to coach to his player's strengths and weaknesses. Instead, he coached to validate his own analysis of what works and what doesn't for players like Adam Oates.
Obviously, Trotz is taking a very different approach. Just seeing how much more pace we play with is such a relief - guys are pushing the play, instead of worrying that they'll get chided for missing a read.
We seem to have cast off the bonds of passivity - hail Trotzsky.