The main things going for the X1 are the Matte screen with larger resolution and possibly better wireless card. Everything else internally is nearly identical with both base models having 128GB SSDs, 4GB memory, and the i5 (although the Air's is slightly higher clocked).
The base model X1 at $1,329 is $130 more than the base Air. If you qualify for the Education discount, then you can get an Air with the 256GB SSD upgrade for $1,349 at Best Buy - double the storage of the same priced X1. Otherwise, you can get the base 13'' Air (with edu discount) for around $1,049 at Best Buy.
It depends if the extra screen resolution and matte screen are worth it for you. I have no idea how the Lenovo warranty works, but according to that image you posted, it seems like they may include a 3-year warranty?
I think the better comparison is between the Asus UX31A and the 13'' Air. At Best Buy, the 256GB SSD version of the UX31A is $1,300, $50 less than the discounted version of the 256GB Air. Also, you get an IPS 1080p screen. The trackpad and drivers are obviously better on the Air, but it's not like the Asus's are unusable. Overall, the Asus UX31A is probably the best ultrabook on the market right now.