Originally Posted by juanmaasecas
IPhone usually has a 35mm focal equivalent lens too, which I think is perfect for a smartphone.
Those are subjective, personal preferences. Your ideal of "natural looking" will not be the same as someone else's. I'd much prefer a phone that had a 50 - 75 mm equivalent focal length, but a ~ 35 mm compromise is more common in phone cameras. Corner definition has little relation to small differences in focal length and your argument there is spurious. It is much more strongly related to aperture, in many cases corners will be sharpest ~ f8.
Different reviews have variously cited both f2 and f2.2 for the S4 lens and the Samsung site doesn't give us any aperture specification. The difference isn't significant though and it hardly matters which is the actual case.
Probably the closest thing to a "normal" focal length is 50 mm equivalent which is considered desirable for general use in conventional SLR cameras because it is the focal length that closely approximates the perspective of the human eye. 35 mm has long been considered a wide angle lens and produces a more distant and reduced magnification image at disparity with the unaided eye.
With the advent of digital zoom, most smartphone designers have compromised on a design that tries to cover a range of focal lengths by using a wide angle lens that people can digitally zoom in to frame (crop) a scene. This tries to be everything to everyone, but sacrifices resolution for convenience. When you "zoom in" this way, a picture is degraded with less resolution and a more apparent grain.have taken to using wide angle focal lengths.
There is no perfect or best focal length. It depends on your usage, subject and personal preferences among other things.