Fanatic, when you say that "Ted was by far the better hitter", you did take into account that DiMaggio was a right-handed pull hitter and the distance to left field in the original Yankee Stadium in his era was 457-466 feet, right? I'm sure that you also knew that it was 490 to center in the original Yankee Stadium, which really must have made Joe D. feel great when he hit a ball 420 feet only to be caught in medium center. And you probably, with your thinking realize that many balls that would have been home runs in other parks, were just long outs in Yankee Stadium, which favored left-hand hitters, not right handers, and was in fact, built for Babe Ruth's swing. Who knows how much better his stats would have been had he played his home games in a park that was fair for right-handed hitters. What I hate about stupid sabermetric stats is that they don't take everything into consideration.
Yes, Williams was awesome with an amazing batting eye and recognition of the strike zone. But you need to remember that DiMaggio had a .325 career average with 393 home runs while playing in a stadium that was built completely wrong for his swing.
I just don't get your question. You ask who is better Ted Williams or Joe DiMaggio. Then you go on to say why you think Williams is better. If you already think that, why ask the question.