A lot of current tennis fans are completely unaware of some of Graf's accomplishments, though, so I thought I'd share a couple of them here
Appreciate your thoughts, Steffi was my favorite women's player growing up.
Your post prompted me to do a little research (warning long post).
Aussie Open 88'
Graf beat def. champ and 4 time GS winner, 25 yr old Hana Mandlikova in the quarters.
Graf beat 18 time GS winner Chris Evert in the final.
Evert was 33 yrs old, she retired in 89. Her last slam win was 86' French.
French Open 88'
Graf beat 18 yr old Gabriela Sabatini in the semis, 1 time GS winner (90' US Open), made 8 GS semis and one GS final.
Wimbledon 88'
Graf beat Mary Joe Fernandez + Pam Shriver on the way to the final, neither won a Slam.
Graf beat 32 yr old Martina Navratilova in the final, 18 time GS winner, defending Wimbledon champ (87'), and won Wimbledon in 90' so she still had some tread.
US Open 88'
Graf had a walkover against Evert in the semis.
Beat Sabatini in the finals.
Olympics 88'
Graf beat Zina Garrison in the semis, who never won a slam but made the Wimbledon final in 90, won the bronze in 88'.
Graf beat Sabatini in the finals.
French Open 02'
Serena beat Vera Zvonareva in the 4th rd, who made two GS finals in her career.
Serena beat 3 time GS winner and def. champ Jennifer Capriati (26 yrs old) in the semis.
Serena beat 7 time GS winner Venus Williams in the final.
Wimbledon 02'
Serena beat 23 yr old, 1 time GS winner Francesca Schiavone in the 2nd rd.
Schiavone finished the year ranked 41 in the WTA rankings.
Schiavone made the US Open quarters in 2003.
Serena beat 7 time GS winner Justine Henin in the semis.
Serena beat def. champion Venus Williams in the finals.
US Open 02'
Serena beat 26 yr. old, 3 time GS winner Lindsay Davenport in the semis.
Serena beat Venus in the final.
In sum -
Graf won 6 matches against GS winners
(Navratilova, Evert, Sabatini x3, Mandlikova)
Serena won 7 matches against GW winners
(Venus x4, Henin, Davenport, Capriati, Schiavone)
Schiavone can't compare to the other names on the list certainly.
Gets even more interesting if you add the next 2 slams.
89 Aussie Open -
Graf beat Sabatini in the semis.
Graf beat Helena Sukova in the finals, never won a Slam but made 4 GS finals.
89 French -
Graf beat 16 yr old Conchita Martinez (won Slam in 94') in quarters
Graf beat 15 yr old Monica Seles, 9 time GS winner, finished 89' ranked 6.
Graf lost to 17 yr old Arantxa Sanchez Vicario in the final (4 time GS winner).
03 French -
Serena beat 23 yr old Amelie Mauresmo, 2 time GS winner, in the quarters.
Serena lost to Henin in the semis - hand chicanery.
03 Wimbledon -
Serena beat Dementevia in the 4th rd, won a Gold Medal and made two GS finals in 04.
Serena beat Capriati in the quarters, Henin in the semis, and Venus in the finals.
Graf gets 3 more wins against GS winners (Seles, Sabatini, C. Martinez).
Serena gets 4 more wins against GS winners (Venus, Henin, Capriati, Mauresmo).
Both won 5 out of 6 slams.
Graf notched 9 wins against GS winners.
Serena notched 11 wins against GS winners.
Ultimately, it's a close call, and you can argue it either way, but Serena gets the edge for me since Venus, Henin, Davenport and Capriati were all in their primes.
Evert, for instance, was clearly past her prime at 33 yrs old in 88', she retired in 89'.
The other Graf wins were either prime/close enough to be impressive.