I think Unreal Engine 3 is the best mobile game engine. Some of the best Unreal Engine 3-powered games are: Wild Blood, Lili, Horn, Infinity Blade series, Real Boxing... (released); Sniper: Ghost Warrior, Morning Star, Bounty Arms, Eden to Greeeen, WeMade's 5 games, BWF's 3 games... (upcoming). The only problem is that you must own a powerful device to have the best experience.
Unity Engine is worse than Unreal Engine 3. However, it also generates some good games such as: Ravensword: Shadowlands, Dead Trigger series, Shadowgun series, Bladeslinger.
With Modern Combat 4: Zero Hour, Havok Physics proves that it is also a good mobile game engine. And from what I know, Havok Vision and Frostbite Engine 2 are also coming to iOS. They are the real competitors of Unreal Engine 3.
However, I think the future mobile game engine is CryENGINE 3. Crytek has released a game called Fibble using this engine, which looks awesome. I think that the future versions of CryENGINE SDKs will support iOS. Therefore, we will see many great CryENGINE 3-powered iOS games in the near future!
For Unreal Engine 4, I don't think it is coming to current iDevices. It might not be the case for future iDevices, but we might have to wait for a very long time!