The few 3-on-3 OT's I've seen in the preseason, players have been cautious, but they were still moving around and trying to get open, and more importantly, when they got any sort of pressure, they capitalized. I think the 3 I saw, only 1 went to a "shootout" while the other 2 ended within the first two minutes if I'm remembering right.
That's been one of my biggest gripes with the AI in the NHL series for the past few years. There's no sense of urgency...ever. Your players, or the computer team's players...no one has any idea what to do. Ignoring even just the general inability of the AI to play defense well, or setup offensive scoring chances that look like more than just random passing, the AI don't know what the hell to do in certain scenarios.
I can remember playing NHL14, and in a lot of situations where the game was 2-1, the AI wouldn't really pressure to score a tying goal. I don't really remember them using timeouts, and most of the time, whatever line happened to be out during the last minute was the line they rolled with. 4th line out there? Screw it, let the big guys give it a shot. They also wouldn't pull their goalie until the last possible moment.
Again when down by a goal, or on the powerplay, there's no urgency to get to the puck. Guys move at the same speed, no matter what they're doing. Guys don't rush to the line trying to keep the puck in, and they don't really play defense any differently, even with a wide open net down at the other end of the ice. They would still lazily skate around the neutral zone, but there was no hustling and rushing. Just like the Blues/Brewers, I'm really hopeful that the next season brings some real changes. The AI in this game has been stagnant, and while I haven't gotten to play any hands on time in NHL16 yet (still hoping to rent it or find it used...game rental isn't fun to do anymore) I also haven't seen anything from the videos online that indicate anything has really changed.
It would be great if the AI 'knew' what the situation was. Down by 1 goal in the 3rd with the playoffs riding on this win? That bench is going to get short, and you're going to be throwing out your top lines until those guys physically can't stand. Your defense is going to pinch more and take risks, and when the goalie gets pulled (which the AI will hopefully do before the 30 second mark, despite sitting in the zone for the past minute) you're going to throw your best scorer out there, and use a timeout when you can, to rest them and give them a chance.
On the opposite side of things, when you're trying to guard that lead, your guys are going to backcheck harder and your defense will spend more time worrying about not getting beat.
This and players that play different would go a long way to making the games themselves feel more unique and alive, and the player separation would help to make the teams play more uniquely. You have to pay a lot more attention in the game when someone like Karlsson or Shattenkirk are out there to help tie a game, instead of the AI sending out someone like Steve Ott to help tie the game.