The problem I have with the GS4 is the AMOLED display. It still isn't bright enough. At full brightness, it is the same brightness as the iPhone 5 at around half brightness. Also, whites are still not white. Part of that is because of the brightness, but even when the brightness of the iPhone 5 is set to the same as the GS4, the GS4 still doesn't look as white as the iPhone 5. (I have them side by side right now. I'm returning the GS4 today.)
The problem is that it has too many green subpixels. If the GS4 is the only device you use, you might get used to it, but I sit at a computer with an LCD all day so I go back and forth from it to my phone. When my eyes are adjusted to the LCD, the GS4 looks ugly to me, but even on it's own, it doesn't look right. Green is too oversaturated.
Even in Movie mode, which is what I've been using, the saturation has a green push because of the higher number of green subpixels. It is very close to an LCD in color saturation, but the green push ruins it for me.