Below are three laptops within your price range from Newegg.
MSI C Series CX61 2OC-206US Intel Core i5 4200M(2.5GHz) & GT 720m - $700
Lenovo G505s (59378837) AMD A-Series A8-5550M(2.10GHz) & Radeon HD 8570m - $530
Acer Aspire V5-552G-8632 AMD A-Series A8-5557M(2.10GHz) & Radeon HD 8570m - $530
The GT 720m and Radeon HD 8570m are ranked close to each other with the GT 720m just slightly higher.
The MSI laptop is more expensive because it has an Intel CPU. Intel CPUs are more powerful than AMD's CPUs (they call them APUs). If both were at the same clock speed Intel CPU would simply outperform the AMD CPU. The AMD CPU is a quad core, while the Intel CPU is only dual core. However, many benchmarks have shown than Intel dual core CPUs can perform just as well or better than AMD's weaker quad core CPUs. However, the price difference is $170 compared to the two laptops using AMD CPUs. The MSI also has 6GB instead of 4GB of RAM; but RAM is inexpensive. The hard drive is also larger by 250GB; but hard drives can be upgraded as well.
The Acer laptop seems to be the lightest of the 3 at 4.41lbs. The other two are basically 5.3lbs. It comes with 4GB of RAM that is embedded into the motherboard. But there is an available slot to add up to a single 8GB RAM stick.
The Lenovo laptop is basically the same as the Acer, but it is not as light. It probably comes with 2 sticks of 2GB RAM. They generally have a better reputation than Acer when it comes to build quality, then again no one has a perfect reputation.