I could assume that Rachmaninoff would probably be the better overall pianist but how could anyone know for sure. Rachmaninoff was probably one of the greatest piano performers ever. He performed his whole lifetime, something most renown composers (even Liszt) never had the energy to do.
The reasons I go with Rachmaninoff are two-fold:
1. Rachmaninoff was clearly more well-rounded. Could read sheet music, could improvise (not as well as Art, of course), probably as technically proficient as Liszt, and his ability to write and understand music of all types (symphonic, chorale, piano) and eras. Rachmaninoff is also a world renown composer - forget piano skills altogether. While he might not be able to play jazz well, I am sure he understood exactly how jazz worked in theory. He was a musical genius.
2. Art Tatum is over-romanticized for the wrong things. He should be remembered mainly for his innovations in the genre of jazz. Not only as a technician.
Art Tatum is truly a jazz innovator. When you compare him to Oscar Peterson and some of the other great jazz pianists his music isn't always as interesting. But people have to remember that comparing Art Tatum to Oscar Peterson is kind of like comparing Beethoven to Rachmaninoff (jazz developed and changed very quickly). Art Tatum, to me, is not just a piano virtuoso or piano performer - he is one of the most influential jazz pianists to ever exist - shaping the future of jazz.
The problem is that Art Tatum is over-romanticized for the WRONG things. People always bring back Horowitz's quote "If Art Tatum ever seriously studied classical music I would quit". My argument is speculation because I have never met Horowitz but I can almost guarantee you that it was meant only as a nice compliment because Horowitz probably realized for the first time in his life that there was something he couldn't play well - jazz.
Art Tatum should be romanticized not for his technical playing per-say, but what he actually did with the music. I would argue that since Rachmaninoff's musical style was out of it's time, that his extreme level of virtuosity was one of the main things that helped immortalize most of his music. It doesn't matter if Art Tatum plays 40 bpm or 180 bpm, as his music, regardless, is the cornerstone of jazz piano. That is why Art Tatum should be remembered as an innovator first and a technician last.
It's really unfair to make me compare the two because Rachmaninoff clearly had no interest in being able to sit down at the piano and improvise jazz while Art Tatum clearly had no interest in the classical repertoire or "formal composition". I personally see Rachmaninoff as a more well-rounded virtuoso while I see Art Tatum as the Beethoven or Bach of jazz. Rachmaninoff was clearly a better pianist than Beethoven (we can know this from the music that they both wrote - also Rachmaninoff had the retrospect of 100+ years of musical evolution) but without Beethoven Rachmaninoff couldn't have ever existed or came into his own. - Without Art Tatum could Oscar Peterson and Erroll Garner be as successful as they were?
So who would win in a duel? Highly opinionated as it depends which music you enjoy more. Both Rachmaninoff and Art Tatum were entertainers and were good at it.
The fundamental problem with this question though, is that Rachmaninoff would have a lot of trouble playing along with Art Tatum and Art Tatum would have a lot of trouble playing along with Rachmaninoff. Art Tatum was the better improviser but many people falsely assume that classical musicians are bad at improvisation because they read from sheet music, but I can guarantee you that most of the renown classical composers could hold their own in improvisation. If you compose classical music, you clearly have the ability to improvise. If you only perform classical music, you probably cannot improvise well, if at all.