Pixel size of the sensor does not affect the output/fished size of the picture taken.
4mp at 16:9 ratio, as in the ONE, ought to output a picture that is 2,666 x 1,500 pixels, or something like that.
13mp at 4:3 ratio, as in the GS4, ought to output a picture that is 4,163 x 3,122 pixels, or something like that.
That's 3.25 times as much area. Now the actual output you SEE when you look at either one depends on the ppi of the screen you are viewing it on and whether any "shrink-to-fit" is going on behind the scenes to get the whole picture visable at once or not. Or, for printed pictures, it depends on the dpi of the printer and whether or not any size manipulation happens behind the scenes - such as would be the case if you choose a default print size from within the default MS Windows viewer - or intentionally by the user.
Keep in mind that on even a 1080 screen like most of the new flagship smartphones have, either picture will be shrunk to fit when you look at it from within the gallery, and if everything else were equal would look pretty dang near exactly the same. Until you pinch-to-zoom, when you will find the larger picture will have much more "zoomability" before looking pixelated.
Now the tradeoff for having larger sensor pixels in lieu of quantity is that although you lose "zoomability" or print size, you gain - in theory, again if everything else is equal - better light gathering. This means a better opportunity for a decent shutter speed to noise ratio in any given lighting senario. Said simply, better indoor or evening photos.
Hope this has been helpful.
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