I think they are both great but not the greatest.
Ben Hogan is by far the greatest! He left to fight in the war for 2 yrs. Had a terrible accident that almost killed him in 1949 - lost 1 yr to that. played the rest of his career on two shaky legs. In 1953 he entered 6 tournaments and won 5 including:
the Masters, U.S.Open at Oakmont, British Open at Carnoustie (his only British Open)
He won 63 tournaments
player of the year 4 times
Vardon Trophy 5 times
Ryder cup as player 41,47,51 undefeated
Ryder captain 47,49,67 undefeated
PGA Champ 46,48
British Champ 53
US Open 48,50,51,53
Masters 51,53
out of 292 career tournaments finished top three 139 times
finished in top ten 241 times
Need I say more?
Ben Hogan was the GREATEST!