FYI, although someone mentioned they weren't shipping until the 27th, there were a few in stock on Amazon (no idea how they were available before Dell was shipping), and I actually received my direct order from Dell yesterday.
I have both my MBA 13 and the XPS 13 side by side so as I transfer my work over to the new unit I can do some comparisons.
Initial impressions: The screen on first look definitely makes an impact. Yes it does have some matte effect but the increase in resolution is fantastic. The near bezel-less design is pretty cool, but for some reason makes the screen feel smaller to me. YMMV. The touchpad and keyboard are both good, but not quite as nice as the MBA. This isn't so much a quality issue as it is that the overall size is indeed smaller so everything is a bit more cramped and the pad is of course smaller.
The footprint is significantly smaller than the 13, as people have noted it's more like the 11's footprint. It's a tiny bit chunkier, which explains the weight over the 11. I thought the weight difference would be more noticeable but it's fairly slight. I'll have to do a comparison with the 11 when I get home. Of course this is the kind of thing that will be more of an impact over an extended period of time, such as for travel or walking from building to building. The build quality feels solid and I do like the black carbon fiber look. Just a matter of personal preference, I guess. I don't think either is better, just different.
General performance feels very fast (file transfers, reboots, wifi are all I've tested thus far) but I have noticed the fan does come on more than I'd expect it to even when copying files. Will have to keep an eye on that.
The big test will be of course battery life. I should be able to tell in a couple of days of normal work use if it is significantly better.
So short version: nothing mind blowing, but so far it feels like a decent tradeoff on keyboard/touchpad in exchange for smaller size, higher res screen, lighter weight and more battery life.