I think 1956 proved Mantle was better than Mays. IF Mantle could have stayed healthy there would be no debate.
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.
Mays had over 4000 hits, over 600 home runs, over 300 stolen bases. And he was the most dominate center fielder of all time (look at the youtube video of his catches). Plus he was a nice guy. Like I said, Mays was the best all around player of all time.