It's all very subjective, but in it's ideal form baseball has several points that elevate it over the other major sports:
1) The game is decided on the field, team against team, man against man...there is no clock, no artificial tie-breaker, no contrived rules where one method of scoring is worth more than another. The game is played the same way in the 17th inning as it is in the First.
2) Ideally, all the players are judged by the same skill set regardless of position...they must run, hit, throw and field up to a certain level in order to compete (I say "ideally" because this is not true in the AL...which is why "purists" abhor the DH).
3) The Game encourages humility and discourages bravado...This goes directly against the NFL and NBA, which seem to celebrate self-promoting loudmouths who prance around like prima donnas and preen and pose simply because they happened to to their jobs. Although I would say that Hockey players tend to be the most "down to earth" of all major athletes, within the NHL game there is still an emphasis on "tough-guy machismo" that is absent in Baseball.
4) The Game combines the best elements of Team and One-on-One competition. It all begins with the Pitcher/Batter duel, but depends on the ability of men to work together in concert...whether it means covering your position and hitting the cut-off man on defense, or advancing the runner into scoring position on offense.
5) Even though there are Superstars, Baseball celebrates the rise of the "working class player." The NFL and NBA are "star driven" games...everyone knows LT and Tom Brady...but where's the love for LT's lead blocker or Brady's left guard? You'd have a hard time missing Shaq or Tim Duncan if you met them at the mall, but would you even recognize Dustin Pedroia or Grady Sizemore if you met them on the street?