How can an iPhone 5 do so much with only a 1.3Ghz Duel Core?

Now I know it is done through optimisation but a 1.3Ghz Duel Core A6 chip can run games better load things faster and I know it doesn't run program's in the background but still against a 1.4Ghz Quad Core Samsung S3 and the 1.6Ghz in Note 2 or a 1.5Ghz Quad Core Snapdragon S4Pro in the Nexus 4 the Nexus 4 is still slower than the iPhone 5 and that is still equivalent to the 1.5Ghz Duel Core Snapdragon S4 processors in the past yet it still manages to wipe the floor with most Android phones I mean it does have and simpler OS but in games it still beats other phones with better processors?

Simple its more efficient. It doesn't need a one GB Video card Costing $500 almost half the cost of the computer and a 500 - 750 W psu enough to heat a small room.

IPhones are phones not computers it doesn't take much power to run iOS anyways. Android is more advanced. All apps are optimized for the iPhone. They're only 20 Mb per app (ram).

Its not all about the numbers, you can have a dual core that will out perform a quad core. It has to do with the architecture of the processor (some having Harvard architecture and other having Von Newman) and how well it manages its resources (memory/registers, etc)

Another thing is the operating system. Apple's OS has been known to run smoother than Android. Again, it has to do with the design. Apple's approach is much more conservative than Google's. This is why advanced users tend to go for android (more flexibility.

As far as the iphone being faster than other phones like the nexus 4. Benchmarks may prove that yes, however day to day usage and the many features of the nexus 4 for example may show that the nexus or similar phones are superior.

Imram is rite, it also has alot to do with the screen size, bigger screen takes more processing power, smaller screens are less demanding so a note would need a bigger processor than an iphone 5,
its main factor is architecture, look at pc's, 2.6 ghz quad core a few years ago would be wiped out by a newer 2.6ghz i5 for example, my wife has the iphone 5 and it is a great piece of kit but i do prefer my galaxy s3 for games, the graphics on games like real racing are much better. Even if the game doesn't load as fast.