The X850XT would win some games but the 7800GS is the better card. I totally agree with Prozac though, look for a cheaper one. They can be found for around $250. If I had to decide just based on those two choices you gave, the X850XT for $60 less would win my vote for sure.
If you got the cash, the 7800GS will last you longer, as it has the SM 3.0, which the old AGP ATI cards DO NOT have. This technology will last you a lot longer than the old stuff on the ATI's, and will make games look a little better, though AGPs are already outdated.
OK, now you are talking; that's a good deal in AGP.
The X800XTpe is actually a tiny bit faster than the X850XT (non-platinum) although it's easier to speak obout them as equal. I have that card and think it's a great choice at the price you found. As far as the power cable, it will use a 4-pin molex connector just like a hard drive or cd-rom drive. If you need an extention, then the 9800xt one will work fine as I believe it's the cd-rom style molex and not the smaller floppy drive connector. Power supply wise i'd think it would require the same as the X850XT. I have used mine in a 4- 80mm fan, 1-HDD, 2 optical drive system with Antec 350W smartpower and a 2 fan, 1HDD, 2 optical drive system with Antec 330W Truepower power supply. What is the 12v rail on your allied 350W? How loaded is your system with drives and fans? What mobo and CPU?