Personally I think a lot of the "play fast" stuff is wishful thinking by the fans. Fans who were tired of Cronin now just want the complete opposite, regardless of if it works. Teams that play fast don't tend to do any better and Brannen has averaged around 150 in pace, so not exactly running all the time.
I doubt the defense will get simpler. Cronin tried to coach just one defense and perfect it. Brannen probably won't have as complicated of a defense, but he will also play more defenses and players will have to learn the subtleties of each defense. Brannen has talked a lot about working on defense during the summer practices.
Offensively, I expect us to push when it's available and take the first open shot. But not to be constantly pushing. As JoeRunner said, few teams have the players to play a pro style where every player (or at least the 1-4) can push the ball. Also I expect to get on players about shot selection and even pull them, NKU had a very good Efg%, doing that requires the right players taking the right shots. If someone who shouldn't be shooting takes a long jumper or a bad three, I expect Brannen to get on them just as much as Cronin would have.
I guess we will see. All we've heard from Brannen is talk so far. Cronin used to talk about pressing and running every year and put more focus than Brannen has on recruiting for that system. And yet come conference play, we almost never pressed. It seems like most pressing teams are long/tall athletes. But Brannen recruited quick guards and big, plodding centers, so it's hard to see us pressing a lot.
I anticipate us playing mostly half-court defense, but focusing more on getting the ball down court quickly on offense. Test the defense, if it's there take the shot, if not pull it out and run the offense. As I've said before, my biggest concern is our rebounding, you can't run if you can't get the rebound.