I don't think it's that lopsided. I think people are underestimating Brett Gardner. He's a elite defensive outfielder, a great baserunner, and has good on-base skills. His WAR over his last three healthy seasons are 6.0, 4.9, and 3.2. He'd be a big upgrade if the Reds think that Hamilton isn't a great defender, and whether his sub .300 OBP would hurt his baserunning value. They could also use him in LF over Heisey/Ludwick. They'd also free up some money, so they could make a run at a free agent starter.
Bailey had a breakout year in 2013, but he doesn't have an amazing track record. He's had a problem with home runs in his career and moving to the AL East won't help. Also, Yankee Stadium isn't kind to flyball pitchers. His HR/9 and K/9 numbers could easily regress to career levels, which would make him more of a mid-rotation starter. He'd still be a huge upgrade over Phelps/Pineda, but consider that the Yankees would be replacing Gardner with a 38 year old Alfonso Soriano. That would mitigate the upgrade the Yankees would be getting in their rotation.
They'd also have to extend Bailey at over $100 million. Between him, Ellsbury, McCann, Sabathia, Teixeira, Beltran, and Rodriguez they have about $140 million locked into 7 players in 2015. Could they afford to pursue Tanaka with that much payroll already committed? I think it might take them out of the running, unless they are going to match the Dodgers in payroll. Also, would a team with that core be any good? I seriously doubt it. I also think that short-term Tanaka and Gardner is a better duo than Soriano and Bailey. That being said, I don't think this trade makes sense for either team.