System 1 lists 2 graphics cards which is strange.
Both systems have a to weak graphic system to play ah2, while 1 might be able to play ok on 2 you probably cant play ah.
My take is you should go for Graphics
Nvidea Gforce 5900XT, 6600, 6600GT,6800GT
ATI X700,X800,X800XT,X850
With the higher model number usually better and not much diffrence between ati and nvidia.
With 128MB or more on board ram. 128 bit memory interface or 256, which is better.
With an Athlon 64 you should get PC3200 (aka DDR400) RAM, not PC2700. The information you put with the systems are verry few, intresting is what brand/specification of power supply, what motherboard, how many fans of what size, what case size/type, brand & type of hard disk, brand & type of RAM, Manufacturer and exact name of graphic board, usable expansion slots on the motherboard, what soundcard, which size / type of monitor.
In your two cases the processor is verry fast and expensive while the rest of the system is cheap and low spec, which overall gives crap performance and does not make sense.
A lot of budget computers are sold stating they have a kick bellybutton processor, but the rest is slow. It makes more sense to buy a system with a average processor and have more money to spend on the rest.
So i would rather look for a Athlon64 3000+(or 3200) Winchester Processor with some better stuff around it, like Audigy 2 soundcard, Gforce 6600GT Graphic card, PC3200 Low Latency RAM, Quality 450Watt Power Supply and a decent motherboard with up to date chipset, like Nvidia nforce4 / nforce3 Ultra, VIA K8T800 Pro/ K8T890, SIS 756, SIS 755, Intel 925X (Intel Processor with this one).
All i mentioned are only examples, try to inform yourself in hardware magazines or web sites. For example
PC Buyer Guide .