Shootouts are a different animal, right? They are simulated breakaways, so both players and goaltenders approach the shootout in a different manner. There's not much time to think when a breakaway is sprung during game action, whereas the shootout is much more studied and strategic.
I would say that most players slow it down in the shootout simply because they can; they're not being pursued by defenders and have time to think through what they're going to do, which can be to their advantage. On the other hand, this gives the goaltender a similar advantage, as he can read and react to what the shooter does. Perhaps, then, there is merit to coming in with speed.
Take Sebastian Aho's shootout attempts this weekend, for instance. On both Friday and Saturday, he utilized the same move, but against Buffalo, he went towards the net with more speed and ended up scoring the first goal of the shootout. On the other hand, there's T.J. Oshie. On Friday against the Canes, he came into the zone wide and was deliberate in making his way toward the net. He still scored, of course, because he's a shootout wizard.