Tiger will always have an advantage over Mickelson in majors. There are two types of players - ballstrikers and short gamers. Every player is more one than the other. I think most great players, such as Woods, Hogan, Nicklaus, Faldo, tend to be better ballstrikers who will themselves to develop a good enough short game to win - who then learn how to manage themselves around a course. On the other hand, it's harder for a short gamer, like a Mickelson or Ballesteros, to develop into a consistently great ballstriker.
Many years back when I used to get tickets to The Memorial Tournament I was able to sit in on a semi-informal "clinic" (really a Q&A session) that Nicklaus held for some of the locals. While his ball-striking ability is unquestioned, it was interesting to hear Jack place almost as much emphasis on "playing smart", i.e., managing one's game, managing the course properly, positioning shots to play to one's strengths, etc. He mentioned that any number of times he gained a shot or two in a round by making the right play (and also losing a stroke or two from making poor decisions). It was interesting to hear that from a guy who most weekend hackers like me tend to think of as a big hitter note that smarts can serve you almost as well as clobbering the ball.