Above is an ultra-magnified shot of the iPhone 4 vs the iPhone 5 screen. Look at the difference in pixel colors.
The iPhone 5 has a Retina display at the same resolution as the iPhone 4 and iPhone 4S. However, it’s still better than the previous screens. It has a higher contrast. Colors and other details show up better as well. The actual images are closer to the glass, because of the handset’s construction (the touch sensors are not part of a separate layer).
At a glance it may be hard to notice some of the differences. Still, just a side-by-side look, or a look by anyone who sees their iPhone 4 screen daily would notice the difference.
The contrast is probably the most notable change (of course aside from the screen size, right?).
You can see a closeup comparison shot here: Jonesblog