Samsung is not a company that designs good products. They are a company that designs good products on paper. Let's go over your list and add a few.
The 1080p 5.1" screen. This is a pen tile screen which is actually a 720p display with some extra green pixels, which sometimes appears to be slightly higher resolution. It should be illegal for Samsung to call this a 1080p display, when it is only 1080p when displaying green. The net result is perceptually better than a 720p display but not as good as a 1080p display. In the real world the performance of the S5 screen in terms of sharpness and color accuracy is equal the iPhone 5S, and any marketing which makes it seem much better is intentionally misleading.
The 16MP Camera. The 16 megapixels refers to the camera's sensor. The sensor is your upper bound of information that the camera can capture. In reality the detail will always be lower than that. The lens of the camera must transmit the information to the sensor, and if the lens has poor resolution (defined by it's modular transfer function performance) you will take a lower resolution photo than your sensor captures. The Galaxy S5 has a camera that is capable of resolving 9 megapixels of detail. This is slightly more than the iPhone's 7.5 megapixels but the iPhone 5S has one key advantage: image stabilization. While both technically have it, the iPhone's image stabilization is around 2.5 times better. The Galaxy S5's stabilization is a joke that was tacked on at the last second.
Image stabilization for the phone basically makes your photos indoors 3 times more detailed and less noisy which is a huge difference. All flagship phone cameras take great pictures outdoors, but only good phone cameras can take pictures indoors. The LG G3, and the iPhone 5S are some of the very few phones that can take excellent low light pictures indoors. The S5 is not on that list.
Here's a comparison, see if you can spot the S5's camera versus the LG3:
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And here's another one, in the half light and low light comparison it's like comparing nuclear weapons against stone axes. There's no question about the difference.
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The 5S also has the benefit of the color balancing flash which is nice.
Killer battery life is incredibly misleading too. The S5 draws a ton of power. In the real world benchmarks have consistently shown that the S5 and 5S have very similar battery life with the 5S having 5 hours 35 minutes and 9 seconds in mixed use tests, and the S5 having 5 hours 55 minutes 34 seconds. The Galaxy S5 has 6.3% more battery life, with a phone that is more than 50% larger (in terms of volume).
What this means is that if you put a battery case on the iPhone 5S, lets say a 2300 mah Lenmar Meridian battery case, it will bring the size of the phone to the exact same as the Galaxy 5S, except you will have twice the battery life.
So really the iPhone 5, has ether 2/3rds the size with slightly less battery life, or the same size with twice the battery life.
Expandable memory.
The Galaxy S5 only comes in a 32GB size max, the iPhone 5S has a 64GB size. This is important, because even though you can pop in a micro SD card to the S5, the 5S has more on chip storage.
Using a micro SD card is a terrible solution and I'm glad Apple didn't include it. Micro SD cards are very slow, even with the fast ones. On the low end you will see speeds around 10MB/s (80Mb/s), on the fast end you will see speeds of 45MB/s (350Mb/s). For comparison on board flash storage is 10-20 times faster.
I have a 64GB iPhone 5S personally and was given a 32GB Galaxy S5 from work. I have to use a Micro SD card with my S5 to meet my storage needs, and even with the fastest one it's terrible. Loading a modern mobile game off of micro SD storage would take more than 50 seconds, while on board flash would take at the most 4.
The iPhone 5S on the other hand also has expandable memory. The Mophie space and storage pack can add 32GB of storage and in a few weeks the 64GB model will arrive. This is a much faster solution than a Micro SD card, and doubles your battery life.
Samsung's decision to limit the 5S to 32Gb was not a good one, and dipping into a micro SD card as a band-aid is a bad solution.
In addition to that with Samsung you get at most 25GB of usable fast storage, which is a tiny amount. With the iPhone you get 62GB, due to the higher amount of space taken up by the phone itself. While you can expand the S5 with an additional 128Gb of slow storage, you can expand the 5S with 64GB of medium speed storage.
The net result when comparing the free space of a Galaxy S5 with a 128GB Micro SD versus a iPhone 5S with a 64GB Mophie pack is that while the Samsung Galaxy S5 has at maximum 21% more storage space, on average that storage space would be 70% slower, which is a huge disadvantage and much less usable.
Conclusion:
There are a ton of other points of comparison but it's worth mentioning that the single core performance of the Samsung Galaxy S5, which is what determines real world performance, is around half as fast as the iPhone 5S, and the graphics performance is around 4 times worse. The S5 needs a quad core to have a slightly faster multi core benchmarks as the 5S's dual core, which makes it much slower in the real world and with any apps. The S5 also obviously has a much less premium feel.
If you really drill down into the specs the S5 has many disadvantages over the iPhone and only 3 main advantages: 1. the weather sealing. 2. the screen size. 3. NFC.
Hope that clears things up a bit.