Edberg was basically a better player overrall than Becker, I don't know how many times I have to say that head to head results is given far far too much emphasis by so so many people. You have to look at all results to make a proper analysis
I think Becker was better than Edberg, and I'd much rather have Becker's career over Edberg's:
1. Becker won Wimbledon at 17 in 1985, successfully defended it the next year in 1986, and went on to a third Wimbledon title in 1989 and also 4 other finals. Edberg's Wimbledon record is good and he did beat Becker in 2 of their 3 Wimbledon finals, but his overall Wimbledon record does not compare to Becker's.
2. Becker's 2 Australian Open titles were at the present location, Melbourne Park, on Rebound Ace hardcourt. Edberg's 2 Australian Open titles were at the old location at Kooyong, on grass courts. Although Edberg beat some excellent players to win his Australian Open titles, Becker played his way into form beautifully in both 1991 and 1996 after struggling earlier in the tournament. Becker's high points at the Australian Open were better IMO.
3. Although Edberg did beat Becker in the 1989 French Open semi final to get to the French Open final, something that Becker never managed to do, is that better than being a multiple time semi finalist at the French Open like Becker was?
4. I think Edberg's US Open career was a little better than Becker's overall, although Becker had his moments too, especially beating Lendl on "his court" in the 1989 final.
5. Becker won 3 masters titles and was runner-up on 5 occasions. Edberg did beat Becker in the 1989 Masters final, an excellent achievement, but overall, Becker's masters career is better.
6. Becker defeated Edberg in 5 Masters Series finals or their pre-1990 eqivalents (1986 Toronto, 1987 Indian Wells, 1989 Paris, 1990 Stockholm, 1991 Stockholm). Edberg defeated Becker in 2 Masters Series finals or their pre-1990 eqivalents (1987 Cincinnati, 1990 Paris) and also a semi final (1987 Montreal).
7. Becker defeated Edberg in 3 rubbers in Davis Cup finals (1985, 1988, 1989), the latter two being rather one-sided and ended in West Germany winning the Davis Cup, unlike in 1985. Becker's performances in Davis Cup finals were rather dominating where he seemed to raise his game to a whole new level.
8. I just think Becker has amazing career highs, highs that are better than Edberg's, while the lows are not too crushing on the whole. Becker also has some amazing wins over world number 1 Lendl in big matches. If I was Edberg, I'd been annoyed about that 1989 French Open final and getting blown away 25-10 by my biggest rival in head-to-head. I also think Becker's style has aged a lot better and he finished his career better in the latter years. Late 1996 indoors saw some of Becker's best ever tennis, especially in the Stuttgart Masters where he played at an insanely high level.
9. Edberg's style is much more old school, and he could have easily slotted into the 1950s and 1960s style of play. Becker's power game represented the tennis of the future, although the serve and volley style was of its time and has now gone out of fashion.
10. If I had Becker's career, I'd be far more content. Edberg's career has too many niggles, i.e. Never winning the Australian Open at Melbourne Park, blowing the French Open final in 1989, Becker's performance in the 1989 Wimbledon final being the best of the winning performances in those 3 Wimbledon finals from 1988-1990, being hammered in Davis Cup finals and a few other matches at Becker's hands, and being on the wrong side of a 25-10 head-to-head. Of course, Edberg can say he was number 1 for 72 weeks compared to Becker's 12 weeks and that he finished as the year-end number 1 twice compared to Becker's zero, but rankings are not as important in my mind as titles and those high points in your career.