A fifth Masters victory for Woods would put him one behind Augusta's greatest champion, Jack Nicklaus, and take him to within three of the American legend's record of 18 majors.
An Augusta National victory by the revitalised McIlroy would make the world No.3 just the sixth golfer to complete a career grand slam.
Both men are veterans of golf's spotlight and able to draw on the lessons they have gleaned from it.
"I don't really need to win again ... (but) I really want to," said 43-year-old Woods, back at world No.12 and seeking his first green jacket since his 2005 play-off triumph over Chris DiMarco.
With a US Open, a British Open and two US PGA Championship titles to his name, world No.3 McIlroy is for a fifth time seeking a Masters green jacket that would complete the majors set.
Only Gene Sarazen, Ben Hogan, Gary Player, Nicklaus and Woods have achieved that feat.
"I would dearly love to win the Masters one day (but) if it doesn't happen this week, that's fine; I'll come back next year and take another crack at it," McIlroy said.
"I am not my score; I am not my results. I've had a healthy dose of perspective this year."
McIlroy previously admitted the Masters "is stressful" and that he can be "a complete prick in the week leading up to Augusta".
His resurgence this year coincides with efforts to make himself a more rounded person, and his day includes mind training, meditation and juggling
Woods and McIlroy enter the 83rd Masters, which starts on Thursday, among the favourites to win from 87 players in the field.
McIlroy is the favourite at $7.50 with Australian bookmakers while Woods is fourth at $15.
However, Woods has not tasted major success since the 2008 US Open, while it has been four years since McIlroy's 2014 PGA Championship win.
Both are quietly confident.
McIlroy won the elite Players Championship last month and has not finished worse than ninth in his seven US PGA Tour starts this year.
In 2018, Woods finished tied sixth at the British Open and second at the PGA before he won the Tour Championship for his 80th PGA Tour title.
"It proved to me I could win again," he said of his wire-to-wire victory in Atlanta.
Even Phil Mickelson - himself a chance to win the Masters for a fourth time - believes Woods is capable of reeling in Nicklaus's 18 majors.
"I wouldn't rule him out," said Mickelson, who won February's Pebble Beach Pro Am.
"To see the way he played the Open and the PGA Championship, greatness is still in him."
