The chip in the iPhone 5s is way more powerful than it needs to be.
qz.com
qz.com
"Going from a 32-bit to a 64-bit chip architecture means Apple was able to double the speed of its mobile chip..."
Um, yeah.
The source article is much more interesting: http://www.anandtech.com/show/7910/apples-cyclone-microarchi...
The A7 appears to have two to three times the instruction width of competing mobile chips, that is, double or triple the number of logic units per core. If you have 100% efficient pipelining (always a big if) that would mean two or three times speedup at the same clock speed.