My Brother plays a mage and he used to respec every other day to play PvE and PvP well. For PvE, fire is capable of out DPSing everything bar Warlocks, however, it provides you no lifesavers whatsoever in PvP, and as a result, you die much quicker. Sure, theres a chance blazing speed could proc - you just delay the inevitable.
Frost builds don't give you as much DPS but do give you iceblock and coldsnap, which are essential tools to save your life in PvP.
Arcane power builds are generally very weak. They give you a few sconds of insane burst, but hen leave you vulnerable and unable to output any real damage untill you regain your AP cooldown.