So the iPad 4 is the new iPad, or rather the new new iPad because the new iPad was first the iPad 3, which has now become the old and discontinued new iPad half a year later. Yeah, it's awkward. But anyway. This new iPad is just the same as the old iPad except it's a little bit faster.
The most obvious place where the difference is apparent is in opening apps. I tried a couple of heavyweights -- Fieldrunners 2 HD and Collins Atlas -- and both opened around 10 seconds faster than on the third generation iPad. That's a pretty significant difference in everyday use.
Place the new fourth-gen iPad on a table anywhere and no one will be able to know it's the latest and greatest unless he happens to see that telltale, teeny-tiny Lightning connector. This isn't a product you can easily show off. Just like the iPhone 4S, it has the same weight, size, and overall design as its predecessor. Even the back panel doesn't give any hint that this is a newer iPad than before.
In practice, the most noticeable difference between third and fourth generation of iPad is how quickly apps launch. It's not so much that the older iPad is slow to launch apps, but the A6X-powered model is consistently and noticeably faster to do so. Light apps (like Notes or Mail) launch only a beat faster, but games and movies were often several seconds faster to open on the new model. It makes for a much smoother experience -- Instapaper used to show an empty shelf for a second or two before populating, and now pops to fully stocked life almost instantly.
For now, one primary way you'll notice that this iPad is better than the last version is in the front-facing camera. Previously, it was a VGA-quality lens (0.3 megapixels). Now it's HD-quality (1.2 megapixels), capable of capturing 720p video. This is key for FaceTime. Apple has slowly but surely been rolling out FaceTime HD video capabilities across all their products. Now the iPad is on board as well.
This is all thanks to the new A6X, a retooled and more efficient version of the A6 processor running in the iPhone 5. Here, it's clocked up to 1.39GHz from the 1.05GHz in the phone version, both having 1GB of RAM. In case you were wondering, yes, it still got quite warm when running through the gamut of tests. We don't consider this to be a concern by any means, but if you found the toasty nature of the third-gen iPad distasteful, you're likely to encounter the same heat here.