Based on head-to-head, Becker absolutely did "own" Edberg. A lot of those wins came indoors in the fall, and Becker was such a great indoor player.
But, in the "big" events, they are basically even.
Edberg leads 3-1 in Slams (2-1 in Slam finals - all Wimbledon)
Edberg beat Becker in the final of the year-end Masters in 1989 - another huge event (what is today called the Masters Cup)
BUT, Becker throttled Edberg a couple of times in Davis Cup, really kicked the crap out of him indoors, and you'd have to include Davis Cup as a "big" event.
So, in the biggest events, they are essentially even (slight edge to Edberg), yet overall, Becker has a dominant edge.
Looking at how powerful and brutish Becker's game was, and how he could dominate Edberg at times, I'm always suprised that they have the same number of Slams, and Edberg actually has more Slam finals (6 wins, 5 runner-ups vs. 6 wins, 4 runner-ups for Becker). And, Edberg made the finals of all Slams and actually won a few clay tourneys in his career, as where Becker did not.
And, their achievements are basically against the same era of players so there is no argument in favor of either one for strength of competition. Becker, though, won his Slams over a longer period (1985-1996 vs. 1985-1992 for Edberg) and I believe he won more Masters series tournaments overall. You could also make the argument that Edberg's 6 Slams are not as "strong" as Becker's because they include 2 Kooyong-era Australian Opens. True, the fields weren't as tough overall, and the AO kind lagged behind back then, but Edberg beat tough players en route to those titles, including Lendl (both in 1985 and 1987), Wilander, and Cash.
Both great players, similar resumes, yet Becker has a commanding head-to-head lead.
I'm always surprised to remember that Edberg lead Lendl 14-13 head to head. A lot of those matches were great matches played on big stages. Sort of an overlooked rivalry.