Aaron was an overall better hitter (by a smidge), but they were both elite. Mays' career HRs (660) suffered from playing a significant portion of his career at Candlestick Park -- it's hard to imagine how many more he might have hit at, say, Wrigley. Mays had more flair, Aaron was more laid back. Leo Durocher had Mays hitting anywhere from leadoff to 5th, whereas Aaron was always a 3-4-5 hitter. Mays is included in most all-time-best-starting-nine lists, Aaron is usually on the second team. Both are among the very best of the very best.
I will say that Aaron was a better all-around player than Mantle.