Of course they're different types of fatigue. I only brought it up because you list baseball playing every day as a reason it's better. Put it this way (just looking at physical effort, not the many skills needed to be a pro ball player) ... How long would John Kruk, Pablo Sandoval, Prince Fielder or David Ortiz last on a soccer field with a good youth soccer team? On a 90-degree, 70% humidity day in Brazil, they wouldn't make it through the jog onto the field for pregame warmups.
Excluding pitchers, baseball players need a day off every month or two. I'm a lifelong lover of both sports, but the fact that elite soccer players have to recover after each game is a point in its favor, not a reason it's less of a sport.
As for 90 minutes vs. 3 hours, you're reaching now my friend. The stoppage time that so many criticize is built in to make up for the few minutes of that hour and a half when play is not active. So in the end, the 90-minute game features 90 minutes of play. A 3-hour baseball game — or 4, more often — features an average of 14 minutes with the ball in play (2010 WSJ study; defining ball in play as starting when the pitcher begins his motion and ending when the umpire makes a call ending the play). That study also found that a typical baseball broadcast shows 88 minutes of players standing still (excluding time between innings).
There's a significant percentage of MLB players who could handle the rigors of international soccer in terms of fitness and exertion. But 100% of international soccer players would have no trouble with a 162-game baseball season.