You're putting Matsui over Rivera, Beav? I would probably put Mo as #1 in my opinion.
I am not saying Matsui is a better player than Mariano, he is just my favorite player. I saw in person the Japanese media he had to deal with, even at a spring training game, and the guy handled extremely wel all the attention and the pressure of his contract and great expectations, which is enormous in NYC. He was the consummate professional, played hurt, never complained, hit in the clutch, and in his prime lefties had a hard time getting him out (he led the AL in BA against lefties one year, if I recall correctly). Before his knees were shot and when he 1st came to the Yankees, he was a good outfielder. He was a consummate team player who did not care about stats, adjusted his swing to the situation and would pull a ball or go the other way as needed. He is cut from the same cloth as Mattingly, Munson, and Gehrig, really the only difference is Matsui never had the opportunity to be captain due to others on the team having seniority over him in pinstripes. But if he had played his entire pro career with the Yankees, there is absolutely no doubt in my mind he would have been named captain as were these other players. Here is a historical list of the Yankees team captains:
http://en.wikipedia.org/wiki/List_of_New_York_Yankees_captains
Rivera, Pettite and Jeter would not be much farther down the list as far as my favorite Yankees, but Matsui is in the top 3. When Matsui retired, Jeter, recognizing what he had meant to the team, issued a statement saying he was one of the best teammates he had ever had.
Matsui received enormous standing ovations at Yankees Stadium when he came back to town with the Angels and A's and there is a reason why.
Regarding Rivera, I think of him as a freak of nature type of talent, which you only occasionally see in professional sports. I don't hold Rivera's rare and unusual talent against him, but to me Matsui was more like the regular grinding type of player who achieved success through equal parts of talent, hard work, pride, guts, determination and moxie, although Rivera has a lot of moxie and has gotten very crafty in his later years.