Brett Gardner and Jacoby Ellsbury are comparable players. Both get on base at similar rates, both own good baserunning numbers, and both play good defense.
Except for this year. Ellsbury's not playing so well on defense this year, and that's why Gardner should play center field and Ellsbury should play in left.
If you examine some advanced defensive statistics, you'll find that Gardner is actually far better than Ellsbury on defense this season. Ellsbury has saved seven defensive runs below average on the year (all as a center fielder), while Gardner has saved three runs above average in center field this season in just 58.0 innings.
Gardner is also much better in center when you weigh the career totals of the two players, having saved 23 more runs above average than Ellsbury in fewer than half the total number of innings played.
Perhaps a critique of my viewpoint would be that Ellsbury makes much more money than Gardner and should therefore play the more demanding position. But as a fan, and a Yankee fan, I want the team to have the best chance possible of winning. Defensive stats aren't perfect, but the easily available ones suggest that Gardner is a much better defensive center fielder than Ellsbury is. Since Gardner is more able to help the team at that spot than Ellsbury is, he should play there instead.
Note: All stats included in this post came from www.fangraphs.com.