that's not as hard a question for an unbiased non yankee, dodger or giants fan if you just pick all the facts apart......
first lets forget about Snider... he simply wasn't in the same class as the other three. Dimaggio couldn't run/field or steal bases like mantle or mays (not that he was bad, just wasn't among the greats in those depts). mays was a better fielder than mantle, he had a better throwing arm than both and ran better most of his career and stole more bases than both mantle and dimag combined. both M&M also hit for more power than dimag but mantle had the short porch in right field when he hit lefty (which was often since there were few lefty pitchers back then). mays played the most of his career on a far inferior team than mantle and dimaggio who played on the power house yankee teams of the 40's, 50's and early 60's. mays also played the better part of his career in shitty candlestick with the winds swirling or blowing in. granted mantle was injured and played drunk most of his career but that's part of the equation.... mays stayed healthier and played longer. mays also missed two years of his prime in military service (52-53) or he more than likely would have broken the babe's record with ease. and not that it matters as much but mays also had to deal with racism on and off the field in the early part of his career in certain cities. mays saw a lot better pitching in the NL than mantle or dimag saw in the AL at the time (koufax, gibson, spahn, seaver, carlton etc...). mays also was the only one to of the four to reach 3000 hits (the others didn't come close), have a 30-30 season, 600 home runs, 2000 runs scored and almost 2000 runs batted in. the career numbers between mays and the others aren't really close. mays had over 1000 more hits than dimag and almost 900 more than mantle. mays had 100 more home runs than mantle and almost double the HR's of dimaggio. dimag gets the nod on the pussy dept, but he threw it away....so?
AVG RUNS HITS 2B 3B HR RBI
.302 2062 3283 523 140 660 1903 mays
.298 1677 2415 344 72 536 1509 mantle
.325 1390 2214 389 131 361 1537 dimaggio
sorry yankee fans but Mays was best and in MHO...it wasn't that close.