You Or Me is just a better (and more digestible) version of the song, with its piano interlude and the non-Bon Jovi chorus. DT has played several demo versions live after official release including Hollows Years, Burning My Soul and, of course, the following alternate versions were previewed before an album release: Change of Seasons, Take Away My Pain, Burning My Soul, Lines in the Sand.
Best I can recall, the only other demo versions that have not been played live are Metropolis 2 and
Pull Me Under (with Erotomania interlude), and be honest, it would be mighty cool to hear that live!