If your Sprint or non-Sprint Galaxy S4 is eating battery life after the official update, then here are some quick tips to fix that issue
Disabling DRM Protected Content Storage in Application manager. Disable or delete any unwanted or unused apps. Lot’s of people are reporting that Media app using an outrageous amount of battery. Consider rooting and flashing a custom rom for better battery life, which you can find on the XDA Forums (although flashing a custom rom will void warranty.) Go into recovery and wipe cache and dalvik cache if you can, that often fixes things. Get the Greenify app which let’s you see which apps are running in background, when you are not running them. You can permanently hibernate an app that is running in background without your knowledge.