Throughout the 1950s and into the early 1960s, it was pretty much the consensus that Mantle was a superior player to Mays. It was only in the mid-1960s when Mantle's injuries really caught up to him that people started to talk about Mays being Mantle's equal. In their best days, I'd take Mantle any day over Mays (but obviously given my screen name, I'm not unbiased in this debate). Of course, because of his longer career, Mays put up superior career numbers. However, in that match, both are beaten by Hank Aaron who played during the same era.
I remember reading the sports magazines at the time. They showed that the Yankees win/lost percentage without Mantle in the line up was startling. Not so much what he did with the bat particularly, but just by the players watching him playing through such pain gave them motivation.
I know that from 1961 onwards, it WAS painful just to WATCH him batting from the left side, and it only got worse.
Phil Rizutto