With Giancarlo Stanton now officially in pinstripes, the Yankees are faced with a nice problem to have. Other than one inning in center field six years ago, Stanton has exclusively been a right fielder throughout his career. But the incumbent right fielder is Aaron Judge, who has played in right for all of his 168 Major League games in the field.
Someone's going to have to shift, but left field belongs to the solid glove of Brett Gardner, as it has for years. So what do the Yanks do?
The answer is probably that "it will work itself out," because these things usually do. There are plenty of opportunities in Spring Training to try Stanton and Judge in both corners, which they almost certainly will, and with too many outfielders for too few spots, there's likely another trade coming. We don't know yet if that might involve Gardner, Jacoby Ellsbury -- who has lost his job but has a no-trade clause -- or highly-regarded prospect Clint Frazier.
While it's fair to assume that Stanton and Judge could split time between right field and designated hitter, that can't be the final answer, either. Other players will see time at DH, especially if they import a caddy for the talented but unproven Greg Bird, and even if Gardner sticks in left field, he'd likely sit against tough lefty pitching. Plus, neither Judge nor Stanton is the prototypical slow-footed slugger; they're capable fielders, too.
So the answer right now is that we don't know how this is going to play out. But that doesn't stop us from taking a look at what the data can tell us.
The case for Judge
It's easy to forget that despite his massive size, Judge has above-average speed and range. Looking at Outs Above Average, our Statcast™ range-based outfield metric, Judge's +6 put him as one of the 20 top outfielders in 2017. (Stanton was -1 for the year, so virtually average.)
If we look at a range chart showing just catches made with a Catch Probability of 75 percent or below -- that is, tossing out the easiest 25 percent that any outfielder should make and looking just at the harder plays -- we can see that Judge's range was slightly bigger than Stanton's.

That in and of itself does not make Judge a better fit for left or right field, but remember that in Yankee Stadium, there's so much more left field. The fence in right-center is just 385 feet away, while the fence in left-center is 399 feet. Though the foul lines are more or less the same (four feet deeper in left), the short porch in right renders more fly balls uncatchable in the first place. (This is part of why Gardner, for several years a plus center fielder, has been necessary in left.)
It's that range that's allowed Judge to make fantastic plays.

Interestingly, it's not that much about foot speed. Both Judge (27.7 ft/sec) and Stanton (27.5 ft/sec) rate as similarly above average (27.0 ft/sec) in Sprint Speed, Statcast™'s top speed metric. But in 2017, it looked like Judge got a little more out of it, and he's played left as recently as '16 in Triple-A, though only for seven games. (Though it seems unbelievable now, Judge was drafted as a center fielder, and got into three games there in the Minors in '16.)
The case for Stanton
This isn't the first time that the idea of Stanton moving to left field has been brought up. One year ago at the Winter Meetings, Miami manager Don Mattingly talked about how the Marlins had discussed pushing Marcell Ozuna to right and putting Stanton in left. It didn't happen, obviously, though clearly the team saw merit to it if they'd spent time investigating the idea.
But really, this argument comes down to how Stanton would best fit in with the current construction of the Yankees' roster. While both Judge and Stanton are likely to see time at DH, it seems clear that Stanton will see the most time there. That's partially because Judge is a somewhat stronger fielder, it's partially because Stanton is 2-and-a-half-years older with several leg injuries on his disabled list resume, and it's partially because Stanton seems to not mind the idea at all.
"I'm fine with it," Stanton said at the Winter Meetings on Monday. "I can bounce around. Wherever they need me, I'm OK with that. I always liked DHing when we played the AL teams in previous years."

Let's assume that's true. If Stanton is more likely to split his time between the field and DH than Judge is, then it might make more sense for him to be doing so in left field. That's because Gardner, for all his skills, doesn't have the arm to play right field, where he has played just once in his career. If Stanton is in left, that makes for an easy platoon setup, with Gardner in left, Judge in right and Stanton at DH against righties, and Stanton in left, Judge in right and another righty at DH against lefties.
If Judge were in left, then he would then have to flip back and forth between left and right when Stanton was at DH, because Gardner would only play left.
Maybe that doesn't matter so much, and maybe in the long run, the choice won't, either. After all, the very good Yanks pitching staff in 2017 had the fourth-highest strikeout percentage and allowed the third-fewest non-homer air balls to both left and right field. In part because of that, Yankees outfielders saw the fewest Five-Star and Four-Star opportunities -- the most difficult catches to make, those with a Catch Probability below 50 percent -- of any team in baseball. 

So that helps, because it's not as though this is a pitch-to-contact staff that badly needs the best possible defense behind it at all times. Either way, both Judge and Stanton are good fielders, both are capable of playing both corners and both will likely see time at DH as well. Between Judge's recent shoulder surgery and the fact that Stanton has played 125 games or more in a season just twice in the past six years, it's likely that there will be some occasions where one or the other simply isn't available, opening up more time for Gardner, Ellsbury, Frazier or Aaron Hicks. 
Verdict
When Stanton and Judge are both available, and neither one is at DH that day, the Yanks will have to make a choice. With strong cases for either side, there's not a slam dunk or a wrong answer here. When that day comes, however, the slightly stronger case seems to be for Judge to make the walk to the other side of the field. He's younger, faster and has better range, and Yankee Stadium's left field is simply larger. Until further notice, it's still Gardner's job. He'll just have a very large teammate to share it with.