Although I really love both and had been fortunate to hear both in concert, for me it is not even close: Horowitz, by a mile, and for artistic, not purely virtuostic reasons.
Why? Although he had a larger repertoire, was a great ensemble player and played with remarkable gusto and panache, I have to agree with the late great William Kapell who felt that Rubinstein was not truly an artist dedicated to totally giving himself to the piano; that although A.R. dearly loved music, he was really more interested in living the good life and using piano playing as a passport to fame--the best wines, cigars, women etc. He was content to play many works lightheartedly in public and coast on his remarkable personality and fiery temperament. He had no reservations performing commercially for Hollywood cinema, and because his live stage concert performances were in effect audience 'love-fests', he often got away with obfuscating sloppy playing by holding down the pedal. (I heard him do this in concert at Avery Fisher Hall in the final movement of the Chopin B Minor Sonata; for another example, go to the live radio performance of the Tchaikovsky Concerto with Rodzinski and the NY Phil on CD.--this is why, unlike VH, Rubinstein refused to release most of his live concert performances) His studio recordings can often be a shade too careful that could make composers of differing periods sound alike, and sometimes even in spots boring (just listen to the RCA recording of the Liszt Sonata).
In Chopin, his separation of the opening notes of the C#Minor Polonaise weakens the impact of the dramatic opening of the piece. Also, I do not appreciate his fluctuation of tempo within the phrasing of the great A-Flat Polonaise. And, unlike VH, he does not play the Scherzos in time. Finally, although often lovely and beguiling, Rubinstein never really had the truly heroic sonority (or technique) of the greatest pianists of the century, such as Hofmann, Moiseiwitsch, Rachmaninoff, Godowsky, Levitzki, Kapell, Gilels and, of course, VH.
In contrast, in terms of solo performance, Horowitz's pianism was far more comprehensive in differing styles--this was due to his remarkable variety of touch as well as tonal control (elements that I feel are frequently overlooked by listeners who are only paying attention to the obvious elements of speed and clarity of articulation). If you disagree, remember that Rubinstein would never program a Scarlatti or Clementi Sonata in his recitals or for that matter, one by Mozart; I have never heard him venture into anything truly modern, such as the Barber Sonata, a masterpiece as performed and documented in the legendary Horowitz recording. Finally, it was Horowitz who would truly challenge the listener with his interpretations (unlike AR who frequently opted for the safe road). Sure, he could often miss the mark (I do not at all care for his rendering of the Clementi Sonata quasi Concerto, and don't feel that with the exception of the 3rd movement, the Schumann Concerto w/o Orchestra op. 14 truly ranks with that composer's G minor Sonata as a great piece of music.) However, when he was "on", the results were so overwhelmingly glorious and transcendent. Just listen to the recordings (esp. the "bootleg" live performances, like the the 1948 Bruno Walter/NY PHIL of the Tchaikovsky, which far surpasses in warmth, vitality and power of the commercial "race against the clock" versions with Toscanini). I have to say, the man was in a league of his own.