Although they have an in-house engine for the Battlefield series (Frostbite), EA DICE has gone with Epic's mega-popular Unreal Engine 3 for the Parkour-inspired Mirror's Edge. According to the development team (via Electronic Arts PR), the reason was that the Mirror's Edge project began early on in Frostbite's development, so they decided to use the more-developed Unreal technology instead.
DICE is also developing "a new lighting solution that truly makes Mirror's Edge stand-out visually." If you haven't had a chance to check out the trailer, do so now.