You've picked a statistic that you knew going in would support your bias. Why not choose, for instance, the third game of the season, and see which conference wins most of those games. No, just count all time wins.
I am not a Big 10 fan by the way, I yell for TCU. The fact is though, the Big 10 has a winning record against every conference. Every Conference. In some cases the difference is huge. The SEC is closest. 6 games. But those are 6 games.