So I spent several hours studying builds and spell rotations for my freshly minted level 80 mage, visiting sites like Elitist Jerks, specialized mage blogs, and looking into programs like Rawr. The result of all that research went into two builds, so now I'm dual-spec Arcane and Frost. The Arcane build is a very standard 57/3/11 build, with a standard spell rotation of 4 x Arcane Blast, followed by Arcane Missile, augmented by Icy Veins whenever possible. The Frost build is a 20/0/51 build, with a minor modification to *not* use Brain Freeze, because a) Elitist Jerks claim that Brain Freeze isn't all that good as it appears to be, and b) there is currently a bug with Brain Freeze not appearing in the combat log, thus any addons alerting you to the possibility of casting that free fireball not working right now. The Frost build is using the Glyph of Eternal Water, thus all measurements were taken with a permanent water elemental.
I then went to test the two builds. First test was against target dummies, using all available self-buffs, but no flasks, food, or buffs from other classes. As expected, Arcane performed better than Frost under those conditions. With my 4k Gearscore, I ended up doing 2.5k dps in Arcane, and 2.3k dps in Frost.
But then I went doing heroics to do a more realistic test of the two specs, and the situation reversed. Of course in a heroic the overall dps depends on the dungeon itself, especially for a mage, because some dungeons have more opportunity for AoE than others. And the result also depends on the rest of the group, because if your tank can't hold aggro, you're not doing as much damage. Nevertheless after repeated runs the overall result was very clear: In heroics I ended up doing more damage with my Frost build than with my Arcane build.
The difference was not due to AoE, and surprisingly not even due to mana management issues, even if the Arcane build is more mana hungry than the Frost build. But the main difference in heroics turned out to be whether you were able to pull your spell rotation off. The Frost build conveniently doesn't really have a spell rotation: You use Frostbolt all the time, and sprinkle in Icy Veins, Deep Freeze, and Mirror Image whenever you can. The Arcane build isn't really complicated either, but depends on building up a stack of 4 Arcane Blast buffs and preferably the Missible Barrage buff to fire off a very powerful Arcane Missile spell. That works fine on target dummies and some bosses, but not so well on trash and some other bosses. On trash the problem is the trash being dead before you get to use your Arcane Missile, and the buff ending before the next pull. On some bosses the problem is various boss abilities either interrupting your spell rotation, e.g. with some form of pushback or stun, or forcing you to interrupt your sequence yourself, by having to move into safety. The effect is the same: You're not getting to cast a fully buffed Arcane Missile as often in a heroic as in on a target dummy.
Now add the additional "safety" features of a frost build, like Ice Barrier, and the AoE being somewhat better due to slowing effects, and the conclusion is that for heroics the Frost build is performing better than the Arcane build overall. Better overall dps, better survivability. The Arcane build would probably improve in comparison if I were doing raids, at it will perform better on some big bosses, but in heroics at the moment it isn't really the boss fights that are slowing the group down.