The processor is better, it is sandy bridge processor (or 2nd generation i5), newer and faster.
The graphic card is faster, GTX 560M is faster than an HD 5870M
The Screen is 1080p compared to 1366x768.
Well the GX660 has the higher CPU clock, but an older CPU, so I would think it would be slower.
The first one has an HD screen, which will look nicer if used at 1080p resolution, but requires more graphics power because of the larger amount of pixels.
The main point for gaming is the graphics chip. It comes down to GTX560M 1.5GB vs HD5870 1GB. These are both mobile chips for laptops, but if the numbers were representing their desktop counterparts (the real graphics cards GTX560 and HD5870), the gtx 560 would be more powerful.
If it were me I would agree with refillable and buy the first one (GT683) for 100 bucks more.
EDIT: At the time I wrote this I didnt see that I would be writing what has already been said, but there, now you have 2 people telling you the same thing. :-)