Color rendering and accuracy
Color rendering is an area where AMOLEDs typically perform very well and the Galaxy Nexus does indeed offer vibrant colors, if you don't mind the oversaturation. TouchWizz-skinned Samsung phones usually have a setting for the color rendering, but it's not available in the purebred Android Galaxy Nexus.
The Optimus LTE resists the temptation to boost saturation and offers more accurate colors. Intertek, an international certification company, measured the accuracy of the AH-IPS display and fount it was three times more accurate (that is the difference between the original color and the color displayed was three times smaller) than the Super AMOLED Plus of the Samsung Galaxy S II.
There are no numbers for the Super AMOLED of the Galaxy Nexus, but they should be similar to those for the S II (or worse as it doesn't have a full set of subpixels per pixel).
There's another factor when talking about color accuracy - color temperature. The Super AMOLED screen shows warmer colors, while the AH-IPS is much closer to true white. LG have something called Mobile Graphics HD Engine, which controls the colors - and it seems to be doing a good job.
Viewing angles is one area where AMOLED displays usually excel and the Galaxy Nexus is no exception. There's a slight color shift when viewed at an angle but contrast remains unchanged.
IPS tries to fix the viewing angle problems of typical LCDs and the 4.5" AH-IPS display on the Optimus LTE is one of the best we've seen. You can look at it at extreme angles and image remains basically unchanged. There's a slight shift of color depending on the angle, but contrast remains unaffected.
Overall, as far as viewing angles are concerned the two displays are practically tied.
We mentioned the importance of screen reflectivity a couple of times already. It affects both contrast, as light reflects off the screen (including the black areas), and outdoor visibility as glare might make things impossible to read off the screen.
Obviously, strong enough light will defeat both displays, but in general the Samsung Galaxy Nexus holds up better. Its screen reflects noticeably less light and, despite being dimmer, remains more legible.
Here's a video that showcases the videos and the reflectivity of both screen.
High-quality AMOLED displays used to be unbeatable in providing the best image quality. The depth of blacks, the rich colors and impeccable viewing angles add up to an experience that's very hard to resist.
LG have gone to great lengths to change our minds though. The 4.5" AH-IPS display on the Optimus LTE (the Nitro HD too) deals with the weak points of the LCD technology and beats the 720p Super AMOLED on more than a few occasions.
The biggest advantage is brightness - it takes a properly lit screen to fully enjoy the actual image quality. Graphics are smoother than PenTile (readily evident in diagonal lines and curves), plus the white balance and color rendering are more accurate.
The Super AMOLED on the Samsung Galaxy Nexus offers the unbeatable blacks and slightly better viewing angles. It has the upper hand in outdoor performance due to its lower reflectivity.
It's very hard - impossible almost - to say which screen you should go for. Screens cannot be chosen separately from the phone and the difference between those two displays isn't big enough to tip the scales either way. The rest of the hardware and the software are bigger factors.
Plus neither the AMOLEDs nor the LCDs are all born equal. There are AMOLED units brighter than the Galaxy Nexus and LCD screens with better contrast than the LG Optimus LTE. Those screens have issues elsewhere though, so you really can't have it all.
The important conclusion to draw from this test is that AMOLEDs aren't always superior to LCDs - you can go for an AH-IPS LCD phone if the rest of the specs tick the right boxes and you'll still have one of the best screens on the market.