While the same display has been used in both tablets, the iPad Air's display (on the right) offers slightly warmer tones. Both displays are equally crisp when it comes to text rendering.
The old and the new - the iPad Air is on the right, the iPad 3 on the left, and the visual tweaks are quite apparent - flatter sides, the straight slab look and the storage capacity isn't mentioned anymore.
The front facing FaceTime camera now offers better performance in low light, making video calls a tad better.
With the dual speaker grill on either side of the lightning connector, the audio output from the iPad Air is much better than the previous iPads.
The redone volume rocker and the slider key. But, the positioning remains the same - on the right side spine.
The camera positioning remains the same, but the design of the back panel is very different. Notice the slightly smaller power key as well.
The design changes on the rear panel.
This is how the two displays compare...the older iPad (above) and the iPad Air (below).