I just switched from an s3 about two weeks ago. At max I would get about 5hrs of usage out the thing before I was running for a charger. My 5s allows me to go all day without needing to recharge it. I get about 11-13hrs of usage out of it before the battery is at 1%.
I personally don't think they need to increase battery life, its far better than most android based phones IMO.
Not sure how you compare 11-13hrs to S3 5hrs usage. If you continuous use S3 with screen on 5hrs is about right. But it is impossible you can get 11-13 hrs using Ip5s with SCREEN-ON. I doubt you can get much more Ip5s screen-on time than S3.
Like many have said, the Iphone usage time in Settings is just a nonsense figure. Usage should mean when you are actively using the phone (i.e SCREEN MUST BE ON). But this usage figure register big values even if you don't touch the phone for the whole day. I suspect Apple didnt include screen on time but this nonsense figure to give a better impression of battery life on iphone.
Android gives "SCREEN ON" time which is much better measure as screen uses the most power when it is on which correspond to when you are using the phone.
In these endurance tests there isnt much difference betw S3 and 5s:
Iphone5s got 54 hrs
http://blog.gsmarena.com/apple-iphone-5s-battery-test/#more-55638
whereas the S3 got 50hrs.
http://blog.gsmarena.com/samsung-i9...n-battery-life-test-concludes-see-how-it-did/