I am not sure whether you guys have question about cores and battery life before you got your S4 …
However before I purchased my Galaxy S4 my friend cautioned me that more cores may drain more battery life so there no need to choose quad core smartphone. I think it was a controversial statement, cus what I knew is that more cores ought to save a cell phone battery life easier and I think quad-core phones can save battery life more than dual-core phones.
Then he tried to convinced me by examples( actually he may find on google). He said a more cores processor just like more cylinders car, though it provide the car more engine power, also the gas it need has increased. Same as smart phone, its cell phone battery need to feed the CPU and many other applications and hardwares. A more cores CPU is faster, therefore it can complete more tasks in a shorter period of time with faster boot time or smoother rendering time, by demanding more battery power.
I against his analogy. The mainly reason why I choose S4 is just the quad-core proccessor as I want to play large cell phone games! Although my S4 battery life indeed not enough for me, but it is because my heavy usage and thank to its removable battery so I got myself a MPJ 7000mAh extended battery for extending gaming time and it satisfy me a lot. Also I compare S4 to my previous mobile phone which has similar devices with S4 with only dual core, S4 even last longer when playing a same game for same time. Because S4 will be turned off if the it is no need of high performance, but when we require a high performance, the OS of S4 will decide to use one to four cores depending on the desired speed!