Which is the better graphic card for gaming?

Since I'm not a qualified graphics card expert, I can't judge myself. But from what I know, is that you should always look at the VRAM (Video Memory), I would definitely recommend the NVIDIA GeForce one, since:

1. It has 1GB VRAM instead of just 256MB (1GB = 1024MB)
2. NVIDIA is just better with graphics cards IMO, lenovo is more specialised in fabricating tablets and other mobile devices.

http://www.videocardbenchmark.net/gpu.php?gpu=FirePro+V3700
http://www.videocardbenchmark.net/gpu.php?gpu=GeForce+GT+610&id=33

As you can see from these benchmarks, they are both very low-end card, so really don't expect anything from them. That being said, the GT610 has double the performance of the FirePro V3700.
Neither card is any good for gaming.

I have an internal graphics card (HD4600) on my CPU that has double the rating of the GT610 and I'm saving for something better because it sucks for gaming.

Don't listen to maxim, Vram doesn't say much. I have a GT630 which has 2GB ddr3 and I can only play BF3 at 720p and low settings. Either way I wouldn't recommend any of them since they are both pretty bad for gaming, but if I had to decide between these two I would say the GT610.