The image above gives you some idea for the two displays, but what is more difficult to appreciate from these 2D images is that the pixels in the iPhone 5 are closer to the surface of the glass than in the iPhone 4. This is because Apple has integrated the touch sensor into the display and not layered it on top of the glass.
Getting rid of an optical layer between the pixels and our eyes makes for a better visual experience. Apple did that by using an in-cell touch LCD in the iPhone 5.
It turns out that the pixels in the iPhone 5 are *precisely* the same size as the iPhone 4 pixels, but the iPhone 5 pixels have better color saturation with more contrast, seen particularly in the blue pixels.
Improving sub-pixel saturation is not difficult, but doing that while keeping the same level of display brightness is. An improved optical stack in the backlight unit, LEDs that are more energy efficient, a bigger battery, etc. are all required to improve color saturation and maintain the same brightness level.
Update 2012.09.26: Chris Heinonen, AnandTech:
Wrapping up, the iPhone 5 display is a whole quantum leap better than the display on the iPhone 4. Contrast levels and light output have both been increased, and color performance is astonishing. The full sRGB gamut is present here, and color errors are remarkably low for a even a high end desktop display. While many were hoping for a move to OLED or some other screen innovation, this really is a huge step up that is very easy to quantify. To put this in perspective, in the past few years I’ve reviewed probably 30-40 different displays, from PC monitors, to TVs to projectors. Not a single one, out of the box, can put up the Gretag Macbeth dE numbers that the iPhone can, and perhaps one projector (which listed for $20,000) can approach the grayscale and color accuracy out of the box.
The best display, period. Impressive.