Difference between x1300 and x1600? Honestly I cant tell you in performance terms. I've never used either one and dont know anyone that has. I can tell you the hardware difference is a faster processor (different GPU chip revision) on the x1600 and a better bus, and more shader units. Theoretically it should be faster. Then of course you have the x1800 and x1900.
Sticking with ATI isnt a mistake. Really there isnt much to recommend Nvidia or ATI one over the other. Same price point cards generally have similar performance, unless you find a deal. I generally prefer Nvidia, and thats where my experience lies, so I'd be glad to make recommendations in that family for you. One thing I CAN say about the ATI x1000 family of cards, the drivers are having serious issues right now. The cards are not performing anywhere near as well as they theoretically should be, and I believe its in the drivers. How long that will last is impossible to say. Nvidia had that problem last year with the Geforce 6xxx series cards, now it's ATI's turn. IMHO, the best bang for the buck these days is the Nvidia 6800GS. It's nearly at the same speed and fillrate as a 6800GT, is relatively the same pricepoint as a x1600 and in most tests blows it out of the water. Again though, thats just my opinion. I'm not an ATI guy. Also, they could come out with a driver update tomorrow that takes full advantage of the x1600 and that performance difference could reverse. Who knows?
As for what PCIe or PCIx or PCIex or PCI express is, it is an improvement of the PCI bus that gives the slots faster communication to the CPU. Thats a very simplified answer, but I dont think you were looking for a white paper on the subject.