Both of you are wrong. Arcane outscales both. Frost isn't far off though.
If you're going to argue that Arcane (which does scale incredibly well - I'll admit) is going to beat good-RNG Fire (hence, played to full potential), you're going to need to provide decent proof. I'm not saying that you're wrong - I'm playing Arcane at the moment and am fully ready to accept that it's surprisingly strong, but Fire parses are still ahead.
In those logs I score 3 top-10 rankings as Arcane on Heroic fights. Aside from perhaps the Council one, I can actually say me ranking that high is more due to the lower number of Arcane parses than there are Fire, but even so, they don't come close to the top Fire parses. My Rank 3 Council would have been ~Rank 17 or something had I pulled the same DPS as Fire.
Granted, I'm not exactly "optimised" to play Arcane - I need Wushoolay's to replace Cha-Ye and I need a LOT more Mastery on my gear, but even so I don't think I'd be competing with the top Fire parses. Time will tell as I do indeed gain more gear, but oh well.