I picked up my Air yesterday afternoon. Upgraded from an iPad 3.
Huge, huge improvement across the board. Obviously the form factor is many times better. It's so much lighter yet still feels premium. Holding it one handed for a good while is no problem. I love the narrower shape, and the big screen seems to fill the whole front of the device (almost), due to the narrow bezels. Captain Picard would be jealous. This is better than what he had.
Let's talk about the speed. In two words, mind blown. For context, I use the heck out of my iPad for pleasure and work. The work side of things is where the 3 was sometimes disappointing. I do a lot of email, big attachments, etc. I view and mark up large, complex PDFs. I create diagrams and figures, and do some document creation as well (to the extent feasible on the iPad). I browse complex websites and have many tabs open at once, switching between them quickly, searching multiple websites for a cheap flight or whatever. The 3 could do all this but there was a good degree of lag, slow rendering (of PDFs and web pages), stalls between switching apps, etc. So I always felt limited as to what I could comfortably achieve on the iPad. I often went back to my PC after getting frustrated with the slowness.
But I've been trying all these tasks out on my new Air, and the CPU never even breaks a sweat. It just flies through all this. Even the built-in PDF viewer, which was never that fast, renders the most complex PDFs (including scanned bitmap docs) in less than a second. Web browsing is also much more enjoyable. All the little lags and rendering delays are gone.
Light users of the iPad may not notice the difference all that much. Youtube video comparisons may not fully convey the speed difference. But if you are a person who appreciates high responsiveness in your PC, and want the same in your tablet, then you'll definitely see the difference in this iPad.
In terms of performance, I feel like Apple has crammed a MacBook Air into my iPad. It's really nice. I expect I'll be able to get a whole lot more computing done on the couch without going to my PC.
The last comment I'll make is that the display is better. Now it's the same resolution, same brightness, etc. But what's better is more even lighting and lower reflectivity. It's nicer to read a book or web page on the Air. It's a subtle difference but it matters to me.