"Things the stats don't consider are the ballparks each played in..."

Frank... the OPS+ statistic was designed to do just that. Normalize the "on base plus slugging" statistic to compare players who played in different ballparks. It is the absolute best statistic with which to compare hitters for that reason.

As it turns out, Mickey Mantle is 6th all time with an OPS+ of 172 (ahead of him are Ruth, Williams, Bonds, Gehrig, and Hornsby. Mays is tied for 21st all time with an OPS+ of 155. He's in good company, tied with Aaron, DiMaggio, and Ott. For reference, Albert Pujols is now tied for 7th all time with an OPS+ of 170, even with Joe Jackson, and Dan Brouthers, obviously two of the greatest hitters of all time.

Bottom line is that Mantle was a better hitter than Mays. Period.

Mantle was also a better fielder than Mays (the fielding% stat has to rule on that one).

Mantle was also at least as good of a baserunner as Mays since his GIDP totals were MUCH lower than Mays'.

I don't know how "clear" it is that most players of the era considered Mays better than Mantle, but the numbers don't bear out that opinion. As I said to begin with, they should be #1a and #1b of the era.