Rob, they both would run the current version of AH at a decent level. Some observations, though: Neither of them tells what brand, power and quality the power supply might be. With an ElCheapo you might fry your entire computer right after the warranty period is over! As ebfd11 said, there's no information about the motherboards either, but IMO that's not as big a problem as the PSU unless you're planning to upgrade or overclock.
Since you seem to have raised your budget by some $200, here's an updated list for a decent gamer built with decent or better quality parts:
PCPartPicker part list:
http://pcpartpicker.com/p/ZLQ6K8Price breakdown by merchant:
http://pcpartpicker.com/p/ZLQ6K8/by_merchant/CPU: Intel Core i5-4690K 3.5GHz Quad-Core OEM/Tray Processor ($236.98 @ SuperBiiz)
CPU Cooler: Cooler Master Hyper 212 Plus 76.8 CFM Sleeve Bearing CPU Cooler ($19.99 @ Newegg)
Motherboard: MSI Z97 PC MATE ATX LGA1150 Motherboard ($89.99 @ Newegg)
Memory: G.Skill Ripjaws X Series 8GB (2 x 4GB) DDR3-2133 Memory ($82.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($53.98 @ OutletPC)
Video Card: Gigabyte Radeon R9 280 3GB WINDFORCE Video Card ($199.99 @ NCIX US)
Case: Cooler Master Elite 431 Plus (Black) ATX Mid Tower Case ($32.50 @ Newegg)
Power Supply: SeaSonic S12II 620W 80+ Bronze Certified ATX Power Supply ($68.98 @ Newegg)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer ($15.98 @ OutletPC)
Operating System: Microsoft Windows 7 Home Premium SP1 (OEM) (64-bit) ($89.98 @ OutletPC)
Total: $891.36Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2014-10-08 06:56 EDT-0400
If you don't want to or can't build it by yourself, do as MrRipley suggested. Ask a local builder shop do it for you using parts you/we/they know are of sufficient quality.