The new MacBook Air is incredible. Apple changed every major internal component and the heat issues, core shutdown, and lock ups have been eliminated.
I use the rev B MBA as my primary Mac. I do everything on it and never have a problem. I know several others that have had excellent experiences as well. I wish it would have been around when I was in graduate school.
The original MBA was full of problems that are well documented. If you want a solid Mac that works great, is beautiful to look at, and will not weigh down your bag, the rev B MBA is perfect for you.
The unibody MB is basically the same components as the MBA. Both have Penryn 45 NM CPU, Nvidia 9400m, 1067 MHz RAM, and a 13" display. The unibody MB is still made from aluminum, but has more ports than MBA and an optical drive. However, the unibody MB has a poor grade display. The viewing angle is horrible on the MB display and darks are grayish purple instead of black. The CPU clock speed is a little slower in MBA, but has double the L2 cache which makes it a nice chip.
The MBA is the future of the MB in my opinion. It doesn't cost anymore to make, well a little more for CPU and display, and is wireless and futuristic.
I own both the uni MB and rev B MBA, and I haven't booted the MB since the day I got my MBA. The MBA is so much nicer to look at, is incredibly capable, and is really fun. I highly recommend the rev B MBA if you can afford it.
Also, the 24" Apple Cinema Display works awesome with the MBA. It has a built in USB Hub, speakers, camera, and power for the MBA just like a docking station. It really makes the MBA feel like an instant desktop.
Good luck with whichever you choose.