New <800 Gaming Build. Need suggestions and feedback.

Well, I tweaked a couple of things in TheBigTroll's build to help lower the price. Overall, you'll get the same performance out of either build.

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i5-3570K 3.4GHz Quad-Core Processor ($219.99 @ Amazon)
CPU Cooler: Cooler Master Hyper 212 EVO 82.9 CFM Sleeve Bearing CPU Cooler ($29.98 @ Amazon)
Motherboard: ASRock Z75 Pro3 ATX LGA1155 Motherboard ($84.99 @ Amazon)
Memory: Patriot Viper 3 8GB (2 x 4GB) DDR3-1600 Memory ($27.99 @ NCIX US)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($59.99 @ NCIX US)
Video Card: Sapphire Radeon HD 7870 GHz Edition 2GB Video Card ($194.99 @ Newegg)
Case: Cooler Master HAF 912 ATX Mid Tower Case ($49.99 @ NCIX US)
Power Supply: XFX 550W 80 PLUS Bronze Certified ATX12V / EPS12V Power Supply ($59.99 @ Newegg)
Optical Drive: Sony AD-7280S-0B DVD/CD Writer ($18.99 @ Newegg)
Total: $746.90
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2012-12-29 21:07 EST-0500)

It may be better to go with TheBigTroll's original build if you would like for your system to retain a little more reliability.

*WARNING*

I have heard of some people that have had issues with the Sapphire HD 7870. Their monitors go black and produce no video. I'm sure Sapphire and AMD have addressed this problem, and I don't believe you'll experience the same issues.

Likewise, older models of the Seagate Barracuda HDD experienced high failure rates due to faulty firmware or something. I'm quite certain this issue has also been resolved with newer Seagate drives.