Jack Nicklaus is the greatest golfer ever, hands down. He played against much better competition because he played most of his career during the time when you had to finish in the Top 60 to retain your PGA Tour card, which produced much better golfers and stronger fields. Not like today's tour where you just have to be in the Top 125 to keep your tour card.
Let's compare Jack's major record from the period of 1962 to 1986 (which spans the time frame of Jack's major wins) and from 1997 to 2010 (which spans the time frame of Tiger's major wins).
Jack time frame (TF): (20) players that won (2) or more majors in their career for a total of (71) majors Tiger timeframe (TF): (10) players that won 2 or more majors for a total of (26) majors.
Jack TF: These same (20) players won (383) PGA and (191) European events. Tiger TF: These same (10) players won (146) PGA and (86) European events
Jack TF: (6) players won 4 or more major's (Player(9), Watson(8), Palmer (7), Trevino(6), Seve(5), Floyd(4)) Tiger TF: (1) player has won 4 or more majors: Mickelson
Jack TF: Jack finished in Top 3 in Majors 25 times. Tiger TF: Tiger finished in Top 3 (10) times
Jack TF: (18) majors. 54 hole position - (8) times ahead, (8) times behind, (2) tied. Tiger TF: 54 hole position - (11) ahead, (3) tied. NEVER came from behind to win.
Jack TF: Won (2) majors in '63,'66,'72,'75, '80 Won (1) major in 8 other years. Tiger TF: Won (3) majors-'00, (2) majors - '02, '05, '06. Won (1) major in 5 other years.
Tiger had the greatest year ever in '00, winning both Opens and PGA. Jack came close to replicating this feat twice. In '72 Jack won Masters and US Open, finished 2nd in British and T13 in PGA. In '75 Jack won Masters and PGA, Finished T-7 US Open and T-3 British Open.
I have had the pleasure of watching both Jack and Tiger play in multiple majors on my home course. Jack in his prime at the '68 Open, "80 PGA, Tiger in his prime in the '03 PGA. I also saw Jack play in the '71 Open at Merion. In his prime, Jack was a much better driver of the ball than Tiger was. Jack was the best driver of the ball throughout his career, where Tiger was only a great driver of the ball from 1999 to 2001 when he worked with Butch Harmon. Since he went to Hank Haney, Tiger can't keep his driver on the fairway. Jack was the best long iron player that game has ever known. Tiger can't be considered a great long iron player, because he seldom ever had to hit them. Mid-irons they are equal. Short irons go to Tiger when became a much better short iron player under HH, but wasn't very good with BH. Scrambling goes to Tiger hands down....but then again, Jack always hit 15 or more greens around so he didn't have to scramble like Tiger did/does. Jack is the better putter by a hair simply by taking in the length of his career, his number of majors and the fact that Jack didn't have the pristine greens for much of his career. Jack had to endure lousy greens from '62 until about the mid-1970's. Tiger has played on nothing but fast and pure greens his entire career
If Tiger and Jack went head to head during their peak years at (10) majors, Jack would win (7) of them and Tiger (3).