I currently own both the S4 and Iphone 5. And I have been using the S4 daily for over 2 months for work and also owned the S3 before that. To me personally, it's not about which phone is better, but which one works best for YOU. I surely can do much much more on my S4 than even a jailbroken iPhone, and rooting and custom roms opens up even more possibilities. I do have much love for android. That being said, I still use my iphone 5 as my personal phone and I'm perfectly fine with it. I could list at least 2 dozen things off the top of my head that my s4 can do that my iphone 5 can't, but that certainly might not matter to another person. iOS to me still provides a more seamless, smooth and polished experience than android. For productivity there is no way you could argue that android isn't superior to ios if you had any real experience with it. But outside of work, my life becomes a lot simpler and the iPhone seems to just "fit" better. If I had the s4 as my only device I wouldn't be disappointed either. The hatred and blindness people have from both sides is ridiculous sometimes.
There are a few changes I wouldn't mind in iOS and the iPhone though:
1) Screen size. I used to be a big proponent of bigger is better since the windows mobile days, but not so much anymore. The 5.0" screen on the s4 is great for media, although in my hands it lacks some portability and can be cumbersome. Even that extra 0.2" over the s3 made a difference in reach for me. I love the size of the iphone 5 when I'm out and about. Something in-between the 2 would be ideal for me. The moto x dimensions look pretty good. I think a 4.0" and a 4.5-4.7" iphone would serve the market perfectly. Android would probably also bode well with a flagship phone with a smaller screen (not these crippled mini versions).
2) iOS. I've been using iOS7 since beta 1. Some nice changes but I certainly think a bit more could be done. My iDevices have always been jailbroken so I know these are well within reach.
- Notification center could have more function to it. Actionable notifications are past due. Gestures should have been added to the notifications themselves rather than just switching between today/all/missed.
- Default apps. Apple boasts app quality and availability (there are certainly still a few ios only apps I prefer over android counterparts) yet they force us to use their own. I think android can get a little bloated with choices which is why I use Andmade Share to cut down the clutter. But ability to change at least some defaults in ios would be nice.
- Data sharing. Apps should be aware of each other at least in some instances. Stock apps are okay in this regard but in some cases to carry out the same action on ios may take up to 5 extra taps as it does on android.
Of course there's more that can be added, but I think this would be enough to significantly enhance ios without changing the core experience. My 2 cents.