Well, it seems you answered your own question, though you then expand this question of fat content to "quality."
"Quality" of butter is subjective. It depends a lot on application. Higher fat does not necessarily mean better flavor or better performance (particularly as an ingredients in things like baking). See, for example, this article, which discusses the ranking of butter in a number of applications. Fat content varied from 80% to about 86%, but that wasn't highly correlated with superior results. The tasters' opinions there came down in favor of the lower-fat butter for applications like pound cake (where they claimed more steam from the higher-moisture content added to lift) and buerre blanc (where they claimed the excess fat unbalanced the flavors of the sauce).
But I think this is probably more evidence that American recipes are likely calibrated to assume butters on the lower edge of spectrum, around the legal minimum of 80% butterfat content.
Anyhow, my personal experience is that processing matters a lot more than butterfat content. In particular, I generally taste a strong difference between cultured vs. "sweet cream" butters. And salt content can make a huge difference. But another thing that came up is storage/wrapping, as fat tends to absorb odors and other flavors, as mentioned in the above article and in a Cook's Illustrated review article that also ranked butters in various applications. I find it interesting that this article is available on the Vermont Creamery website, which makes a big point of how it has the "highest butterfat content you can obtain when making butter" of 86%; even they are posting an article whose title is basically that butterfat may not matter as much as other factors.
(By the way, I'd personally disagree with the CI characterization of cultured butters in general as having "artificial, margarine-like" flavors. But everyone has their own preferences, and I think American palates have shifted to expect "sweet cream" butter.)