I couldn't find a better gaming PC for under $600. However, you may wish to consider the following:http://www.newegg.ca/Product/Product.aspx?Item=N82E16883227457
The CPU is better and the graphics card is better.
However, the MAIN reason I recommend this is because the i5-3570 is quite a good CPU and if you want to simply add a better graphics card in the future you can and won't be bottlenecked as much as the FX-4100.
Your choice of gaming PC is very good for the budget, and will play many games nicely. The only alternative I could recommend was $140 more. I would be guessing at an average 20% improvement (it varies between games) and the i5-3570 is a little more future-proof for adding a better graphics card in say two or three years to extend the life of your PC.
Both choices have their Pros and Cons.