DisplayMate posted an in-depth review of the Galaxy S6 (and GS6 Edge) displays, and they find that this display offers several significant enhancements over the Galaxy S5 display. In fact the GS6's display is the best mobile display ever tested at Displaymate, together with the display used in the Galaxy Note 4.
The most impressive advances over the GS5 are the high density (577 PPI over 432 PPI), higher resolution (2560x1440 vs 1920x1080), a 27% improvement in absolute color accuracy, higher brightness (12% improvement) and higher readability and contrast in high ambient light.
Interestingly, DisplayMate finds the new display to be 20% more efficient compared to the GS5 display. It's great to see Samsung making their AMOLED displays so much more efficient every year.
Regarding the S6 Edge, DisplayMate finds that it essentially performs on par with the glass based GS6. This is not surprising as we've seen the same results with the Galaxy Note 4 and the Note 4 Edge.
Finally, DisplayMate compares the GS6 OLED to the LCD used in the iPhone 6. The OLED display offers a higher density, significantly higher peak brightness, significantly higher contrast ratio in both low and high ambient light, significantly higher absolute color accuracy, significantly better viewing angel performance, and has 4 selectable screen modes instead of a single fixed one on the iPhone.