From a Gizmodo camera test:
"This is a relatively easy photo, and all of the cameras perform admirably,
with the Samsung Galaxy S4 trailing the pack. It’s pretty tough to tell the difference between iPhone 5 and 5s, though the newer shooter appears to have slightly better dynamic range from this vantage. In this particular situation, we prefer the iPhone 5s to the usually excellent Lumia 1020 because the photo’s sharpness. The HTC One is out because of some noticeable artifacts — that’s the downside with cropping from a relatively low-resolution image.
iPhone 5s Camera Battle: A Stand-Up Camera That Doesn't Stand Out | Gizmodo Australia
I don't really want to discount this article, because I have not used an iPhone 5 or 5s myself, so I have no personal experience to reference, however when I see articles like this, I always wonder what specific settings were used when the pics were taken... Based on my own knowlege of the S4 (because I own one), I know that there are lot of configurable options on the camera, as well as quite a few preset modes...yet this article does not mention anything about that. When taking pics with the S4, was the camera set to default automatic settings, or something different? And yes, you could probably ask that question about each phone camera they reviewed.
Now, simply using each device's out of the box default settings would be reasonable, but doesn't necessarily ensure that you'll always get the best picture (though I suppose you could possibly argue that it demonstrates which phone has the best "auto" mode?). Changing particular settings may give an unfair bias to one device over another.
I guess my point is that the scientist in me simply doesn't take findings like this at anything more that face value. I want to know what how the control group was established, I want see large enough sample sizes to make results relevant, and I want all variables well defined and accounted for.
And yes, Gizmodo does seem to favor iPhone over Android in my opinion...but I discredit this source long before even considering that.
My own opinion is the the S4 camera is pretty sweet, and certainly more than adequate for my needs. Is the iPhone 5S camera better? Maybe it is...maybe it is only in certain conditions...maybe it's not better at all. I'm willing to bet that when all is said and done, the second statement is probably the closest to accurate, but it doesn't really matter to me...even if the 5S camera was remarkably better I'm certainly not going to buy one for that reason alone.