"I think that over the course of my career, I've had a few," said Woods, who reclaimed top spot in the rankings from McIlroy for the first time since October 2010 last month. "Certainly Rory is this generation's.
"I've had Phil (Mickelson) and Vijay (Singh) and Ernie (Els) and David (Duval) for a number of years, and now Rory's leading this new, younger generation."
McIlroy is good friends with Woods and the pair use the same equipment following the Northern Irishman's controversial multi-million pound switch to Nike earlier this season, but the 23-year-old had earlier played down talk of a major rivalry.
"I don't see myself a rival to Tiger or to anyone," McIlroy said. "Tiger obviously has been on tour for what, 12 more years than me or something like that.
"When you speak of rivals, you tend to put rivals (together) who have had similar success. He's got 77 PGA Tour events, I've got six. He's got 14 majors, I've got two. If I saw myself a rival to Tiger, I wouldn't really be doing him much justice."
Woods has been stuck on 14 majors since winning the US Open in 2008, his quest to break Jack Nicklaus' record of 18 sidetracked by injuries, loss of form and a sex scandal in 2009 which cost him his marriage.
Swing changes made to protect his injury-prone left knee under the guidance of Sean Foley have paid off with three wins already this season, while a recently confirmed relationship with skier Lindsey Vonn seems to have contributed to a more relaxed demeanour off the course.
And although Woods spoke of the "beautiful juggling act" of coping with family life as well as playing golf, he insisted he is still as focused as ever on winning 19 majors or more.
"I would like to be able to get to that point. It took Jack a while to get to 18, all the way until he was 46 years old. So there's plenty of opportunities for me," added Woods, whose last Masters victory came back in 2005.
"I put myself in the mix here every year but last year, it's not like I've been out of there with no chance of winning this championship. I've been there and unfortunately just haven't got it done. I've made runs to get myself in it. I've been there in the mix on the back nine, either not executed, not made enough putts or didn't take care of the par fives or whatever it may be.
"But the whole idea is to give myself opportunities and, as of right now, I'm tied for second on the all-time win list here - he and Arnold Palmer have four, Nicklaus won six - so that's not too bad, either.
"That's one of the neat things about our career, it's so long. We have an opportunity to play basically 30 years solidly at a high level. We have very expansive careers and I feel like I'm basically right in the middle of mine. I have a lot of good years ahead of me and I'm excited about this week."