Super AMOLED screens have always had incredible contrast and color range, but despite this the colors displayed by Samsung's panels have always felt a little bit over saturated. With colors that seemed too good to be true.
The richness and vibrancy of the colors made a lot of people buy these phones. But now that IPS LCD panels have started to deliver increasingly higher contrast for their colors, while also having very high color accuracy, some customers are starting to prefer them. Samsung must've seen this coming a long time ago, and so they strived to fix this issue on Super AMOLED displays.
The latest panel in the Galaxy S4 has just won an award from Underwriter laboratories, because it's one of the most accurate displays around with 97% accuracy on the Adobe RGB spectrum, which has 30% more colors than the sRGB standard. I don't think that's the highest there is, as the latest iPad and iPhone panels have been very close to 100% accuracy, but for a Super AMOLED display this is a great achievement.
The display was also praised for its performance in bright sunlight, although IPS LCD panels still tend to do significantly better in sunlight right now, which may be because of a management decision based on the fact that Super AMOLED displays consume more power if used at a higher brightness, so they try to keep them at lower brightness. That's why they are probably not the best in sunlight, and not necessarily because there's something wrong with the way Super AMOLED displays reflect the light.
However, it's good to see that Samsung has kept trying to improve the Super AMOLED technology, and have continued to work on improving the "Pentile Matrix" (not actually named like that anymore), too, by changing its sub-pixel pattern to a diamond-shaped one. If they keep this up, they may be able to show eventually that AMOLED displays can make LCD's obsolete, but that will be an uphill battle, because LCD's have kept improving fast each year, too, and they also tend to have a pricing advantage, at the same resolution.