Do you have the white phone or blk phone? At best buy and att they have both models side by side and the white is better on the blk phone. I have no idea why but its the same on both phones at two different locations.
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The strength of AMOLED panels lies in their ability to produce deep blacks. Their weakness is usually color accuracy, most noticeably in white areas. If you put an AMOLED panel next to a white reference (the bezel of a phone, for instance), it will look off. On the other hand, because they produce blacks so well, having a black bezel doesn't diminish their quality at all, and will probably show better
perceived color accuracy on white screens since there is no color reference next to the display. That's why when I bought my phone I made sure to steer clear of the white fronts.
However, the Moto X does have a pretty darn color-accurate screen when compared for an AMOLED display. The problem is that when you're comparing to other devices, a) they may be inaccurate in a completely opposite direction, thus heightening your perception that your screen is off, and/or b) the Moto X display simply isn't very bright when set next to IPS displays, which might make it seem dull or dim.
Check out AnandTech's reviews of the Moto X (
AnandTech | Moto X Review) and the iPhone 5s (
AnandTech | The iPhone 5s Review) displays.