I'm auditioning an S4 and its screen (OLED?) may be the best I've seen on a phone. I'd love it if Samsung could marry a screen with that pixel density/quality to their Note 10.1. If OLED has shortcomings they're not evident in the S4's screen.
Here's what I've found with the AMOLED screen on my Galaxy Nexus - black levels are great, and it's more power efficient, but colors on those screens can be oversaturated (depends on how it's calibrated), and the screen wears unevenly - if I rotate my phone (which I rarely do), the left (normally top) side of it has a bluish tint. (note that it normally displays the black status bar on top - so most of those pixels aren't lit up)
Also, note that the S4's screen is pentile while the HTC One's isn't. I've played with both, and the One is noticeably sharper. (I could see the pixels on the S4 when I looked a little closer, though not as easily as with my gnexus. I couldn't from the same distance with the One though.)