From what I can see in Cassidy's seven games, the main components of the style change seem to be:
1. Getting the D men more involved in the offensive zone. Cassidy seems to want them to pinch more frequently, or even cycle down into the circle when they've got the puck.
I think they were very aggressive (and effective) pinching this year under Julien too. The bigger difference to me is defenseman trying to make plays passing and skating the puck out of their own zone, and defenseman being more aggressive getting involved in the rush and getting further up ice during breakouts.
I don't have the data to back it up, but their transition game seems to be much more effective in getting zone exits with possession, at the expense of some defensive zone turnovers.
edit: Which makes me wonder why Colin Miller is still being healthy scratched by a second coach. Either he has had a nagging injury all season, is a complete garbage person, or this organization is horrible at judging their own talent. He's signed through next season so it's doubtful they're trying to suppress his future contract value. Which would be a terrible thing for an organization to do anyway, on several levels