Apart from the screen, the biggest thing the Air has going for it (over the mini and standard iPads, anyway) is the Smart Connector wedged into its left side. This is the first time Apple has built one of these into a non-Pro iPad, and for most people, it basically just means you can magnetically attach a keyboard. (Seriously, there are hardly any accessories that make use of this port.)
In fairness, Apple's Smart Keyboard is perhaps the best non-Bluetooth keyboard you can use with an iPad like this, and I've written nearly all of this story on it (with essentially zero drama). There's little question that this keyboard, and the few accessories like it, make the iPad Air better for getting work done. Just be warned that this luxury will set you back an additional $160.
My colleague Nate didn't find the Air all that exciting when it was announced, and I'm inclined to agree with him to an extent. As genuinely helpful as I've found the Air so far, there's little new ground broken here -- you'll mostly find a bunch of very practical refinements and choices made to manage costs. That's not necessarily a bad thing, though.
I think the fact that the Air exists in this form is important, if only because the existing performance and price gap between the standard iPad and the Pros was begging to be filled with a capable mid-range option. And honestly, after using the Air for a bit, it still ticks off more boxes for me than the mini does: the screen is spacious and pleasant enough to look at, its design is at least somewhat more modern, and the Smart Connector adds at least a degree of flexibility.