Dr. Nick: Seeing her old rival give up at the end like this, is Rei perhaps thinking... "Pathetic?"
Literary Eagle: Heh, that's a good joke! Although just in case anyone is actually curious, the official book The Essential Evangelion Chronicle: Side B shows that Rei and Kaworu are not enemies. I discussed that topic in this short article: Teammate, sympathy?
UrsusArctos: As noted in Cut 114, it's third-tier canon, and the question mark leaves a lingering mystery about her feelings. Perhaps the Duel of the Seeds is just that: headcanon, and Adam and Lilith/Kaworu and Rei aren't really enemies or rivals, but are they truly friends?