kkiwi855 Between the two options, I would purchase the 6GB version over the 3GB. I believe that the 6GB variant has 10% more CUDA cores, therefore is 10% faster. Also it's future proof for games, when you have the texture settings turned up to "ultra".
However.... There are two factors: The next generation of Nvidia graphics cards are "rumored" to be announced in two months. I would assume that the GTX 1170 and 1180 models would release first and the 1160 would be next.
The other bigger factor: If you're intent on purchasing a GPU now (you can't wait), and the 3GB version of the 1060 fits more comfortably within your budget then I suggest that you consider buying a used GTX 970 off of Ebay. With that option, you'll get 3.5GB of usable VRAM, and can get a comfortable overclock; 100 and 200 MHz on the core and memory respectively, if memory serves me right. I'd try to get a GTX 970 for $150 USD or less, depending on what the 1060 models were going for. Just my two cents....