Chad Jennings took a look at this question and asks if swapping them would make you feel different about the roster.
This isn’t to debate the defensive merits of the two outfielders. I’m just wondering if the speed were coming from a typically speed-based position and the power were coming from a typically power-based position, would the lineup seem better? It seems there is some debate about whether Gardner provides enough power to be a left fielder, but I don’t see that it matters. If he were to open as the Yankees left fielder, he would be batting in the same spot in the lineup as on opening day 2009. The fact he would be playing left instead of center only means the Yankees defense would have improved.From this perspective I see no difference. As long as they're both producing like they're supposed to at the plate I don't care whether it's the center fielder or left fielder that hits 30 homers or steals 30 bases. But based on defense I'd rather see Gardner in center. While they're both good defensive center fielders you could argue that Brett Gardner is better (2009 UZR/150: Gardner: +15.4| Granderson: +1.6), and with his speed he can cover Yellowstone.
So that's what I would do, but now I want to know what you'd do. Who would you start in center?