Mays over Aaron.

OPS+ is On Base Plus Slugging adjusted for the batter's home park.

seasons OPS+ >= 140 and led league and high and career:
Aaron: 19  2  194  155
Mays: 16  6  185  156
Mantle: 16  8  221  172 (highs: 221, 210, 206, 195, 188)

A friend was challenging my contention that when they were playing Mays was universally considered better than Aaron.  Now Aaron seems to be considered better.  A bit like the current Cabrera v. Trout debate I decided to isolate on batting.  I figured if Mays holds his own in the batters box, he beats Aaron because of his edge in fielding and base running.  I threw in Mantle for additional perspective.

I'm sticking with Mays over Aaron.