He also refused to run against her for two other reasons: (1) Her positions are NOT all that different from his (reference Rudy’s own comments when Slick was President comparing Slick to Rudy), and (2) He did NOT want an open liberal Senatorial voting record set in concrete for the public to see in his current quest.
Both valid, but I think the biggest reason was that he knew he would lose. Keep in mind that prior to 9/11, nobody talked about Rooty running for president (why his failures leading up to that day made people think more of him is beyond me).