OK Matt, I'm going to have a little fun.
Doesn't what you stated above argue that Tiger is simply better than Jack in that fewer players have stared him down and beaten him head to head? 19 second places tells me Jack had trouble closing.
Which doesn't make the players around him great-in fact if he had a better short game many of those "great players" would be less majorless-therefore not great.
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Jeff:
Depends on your definition of closing. I think Jack's record of 19 major runner-ups is one of the great under-rated accomplishments in golf, given that he won nearly that many majors.
For the record, Jack finished an average of 2.6 strokes behind the winner in his 19 runner-up finishes. (I counted as three strokes his 71 to Trevino's 68 in the Merion playoff in '71.) Interestingly, he finished one stroke off the lead, as a runner-up, only four times -- twice to Trevino ('72 at Muirfield, '74 at Tanglewood), once to Watson at the Masters, and once to Sutton at the PGA.
Jack also finished 3rd in a major nine times, with an average stroke margin behind the winner of 3.5. (Interesting little tidbit -- if you take out his 3rd-place finish that was 11 strokes behind Floyd's romp at the Masters in '76, Jack's average 3rd-place finish was 2.6 strokes behind the winner, or the same as his runner-up finishes.) Jack finished 3rd in a major a remarkable four times when he was one stroke out of a two-player playoff ('63 and '75 BOpens, '67 and '77 PGAs).
As for closing, one definition might be being tied for, or behind, the lead entering the 4th round of a major. Jack won seven of his 18 pro majors coming from behind in the 4th round, and three more when he was tied for the lead going into the final round. He never lost a major in which he was leading alone heading into the last round. Twice he was tied for the lead after the third round of a major and lost -- to Coody at the '71 Masters and, memorably, to Watson at Turnberry in '77.
Tiger, I believe, has never lost a lead in a major when he was ahead after three rounds. But I also don't think he's ever come from behind -- that is, not in the lead after three rounds -- to win a major. He's had by my count four runner-up major finishes -- with an average stroke margin of 1.5 strokes behind the winners.