The difference between MLB and the other three (major) leagues is that, even though all three have their own experience with mergers, they all merged into one united league. Technically "Major League Baseball", up until the last 20 years, was an umbrella organization supporting two independent leagues. So league-based awards have always had more meaning than, say, AFC/NFC or Eastern/Western Conference awards would.
That said, the first ten (or so) Cy Youngs were awarded across both leagues. So there is a precedent.
The easiest choice on that list is 2004, because Barry Bonds. That was the year he was intentionally walked 120 times, essentially breaking the sport (as I've heard it put).
In 2005, Alex Rodriguez was slightly behind Albert Pujols in average and OBP, but beat him in pretty much every other stat (including stolen bases: 21-16). He also was playing a quality third base compared to a quality first.
If there was ever a Sunday morning hangover in MVP voting, that was 2006. Just making the WAR comparison, at least Ryan Howard finished in the top ten in his league (tenth); Justin Morneau finished 19th. But this isn't a "pick a new guy" exercise, so out of the two Howard had the better overall case with 58 homers and an almost 1.100 OPS.
Jimmy Rollins had an amazing year in 2007, playing every game, 88 extra-base hits (including 30 homers and 20 triples) and good defense at shortstop. Rodriguez ended up with 54 homers and was an average defensive player.
Dustin Pedroia was the hot name in 2008, winning the Rookie of the Year in 2007 and having a better year the next season. He played good defense and led the AL in hits. But Albert Pujols had another Pujols year, with 37 homers and leading the leagues in OPS (and OPS+) despite missing 14 games.
2009 saw Joe Mauer's ridiculous year (one may have even called him Mauer with Power...). He hit 28 homers, but was also the baseball batting and OBP champ while playing catcher. Even another amazing Pujols year doesn't trump that.
Joey Votto and Josh Hamilton had very similar offensive years in 2010. Hamilton was the baseball batting champ, but they ended up with similar OPS and home run numbers. Hamilton played a fine year in left and center field while Votto was average at first, so Josh pulls ahead.
Justin Verlander had a season for the ages in 2011. He led MLB pitchers in innings pitched, strikeouts, ERA+, hits/9, and even wins, and was the AL ERA champ. Ryan Braun had both 33 homers and stolen bases, and led the NL in OPS. The ace beats out the Hammer.
In 2012, since I can't pick Trout, it is Miguel Cabrera's sport-leading 44 homers and .999 OPS versus Buster Posey being the batting and OPS+ champ for both leagues. Similarly to 2009, the production coming from the quality catcher beats out the other position player, especially one who had a significantly negative impact defensively.
Finally, Andrew McCutchon had a great all-around season in 2013, even though he didn't lead the league in any major category, let alone the sport. Miguel Cabrera, on the other hand, led the sport in average, OBP, slugging, OPS and OPS+ to go with 44 homers. That gets my vote.
