I think part of what leads to DiMaggio being overrated is the greatness of his first few seasons. After that everyone looked for greatness out of him, and while what he delivered was only good, the inherent bias made him feel better than he was. I'm guessing if he had the same career numbers more evenly distributed he'd be seen as far less great.
As far as Mays goes, it is all about the walks. Granted, I'm not old enough to have seen him play. That works both ways - I can't see some of the things he did (except on old games that get broadcast periodically on ESPNClassic or used to be on the MLB network), but on the other hand my view of his actual statistical achievements aren't clouded by selective memory of great plays. Mays played at just the right time to maximize his nostalgia value right now. There are plenty of living baseball fans who watched him play, but it was far too long ago for anyone to remember anything but the highlights. So he gets blown up in people's minds. I'm not saying he wasn't a great player. But given that OBP is the most important offensive statistic in baseball, an elite hitter who doesn't walk is giving himself a huge liability. I would take Mays over Musial or Aaron, but I'm not sure I'd take him over Mantle. I'd take a healthy Mantle over Mays in a heartbeat. You just can't be a top 5 hitter of all time with a career OBP of .384, and yet many baseball fans - probably a solid majority - would place him in their top 5. I would easily take Ruth, Cobb, Williams, Gehrig, Hornsby, or even Bonds over Mays. Would also consider Foxx, Pujols, Jackson, Speaker, or Ed Delahanty to be similar. All of the players I listed except Delahanty have better career OPS+ numbers than Mays, and that's ignoring the fact that in the underweighted aspect of OPS (the OBP), all of those guys blow him away. That helps negate his defensive advantage over most of the hitters I listed. Though FWIW, a healthy Mantle is a similarly elite CF, and someone discounted that earlier in the thread.