Battery life of iPhone 4 reduced dramatically since iOS 7
There of course are more power efficient operating systems for a couple of reasons.


Some operating systems take alot of space for themselves to actually run the system
Apps might not always be turned off but suspended, leaving them running


And one of the major battery eaters (not because of OS) is the screen. Turning down the brightness to half-way from full can save about 2-3 hours of battery (sometimes more).

A good solution to the background app problem is exiting the apps by pressing the home button twice. You will see the apps you have active. You can swipe up to exit the apps, and home button or tap on an app to go back to it. However that no longer works.


  Quitting apps is not the way to do it. The old 'slide it off the screen' does nothing whatsoever unless an app is hung etc. Backgrounded apps set to no refresh was the replacement for that old voodoo, since iOS 7


-Tetsujin

Basically, that solution used to be a thing, but now background apps do not seem to be the issue at all anymore.



Just as some extra information, Androids have custome ROMs (OS) that attempt on being more lightweight operating system clones of android. However custom ROMs have yet to exist on Apple phones



Sudden battery drain is also not only a software problem, but it could be a hardware problem too. To maintain battery health, make sure to charge with your native adapter (not other ones for different phones), as sometimes they have higher voltage, therefore harming the battery. If suspending apps does not resolve your battery problem, you might want to bring your phone for a battery checkup just in case.



And finally, to answer your question with battery packs, there are some good ones. You can get ones in a separate "power bank", where you connect your phone and charge, or you can get ones that are built-in to the iPhone case, like in the example below:


Of course, there are also iPhone 4 cases, not just iPhone 6 ones.