Is the Sapphire Radeon R9 270X 4GB an acceptable substitute for the Gigabyte R9 270X 2GB?

I'm supposed to be buying parts to build a Minecrafting (playing AND recording) computer for my kids, but the guy who's building it didn't give me a list of parts. So I'm going off of this list: http://elitegamingcomputers.com/how-to-get-a-computer-for-minecraft-without-spending-a-ton-of-money/ (the $500 build). But the video card listed, the Gigabyte, isn't available via Amazon Prime, and I really need it to be. I noticed the dimensions are different, but the Sapphire is actually smaller, so I don't imagine that would be an issue. I just don't know about the differences in performance and such, since one is a 2GB & the other s a 4GB. Some of the articles I read said that a good graphics card is the most important part of the build, so does that mean that the Sapphire would be better? I really have no idea what I'm doing, and could use the help.

As long as they both have GDDR5 memory then the 4gb is the better deal. Also look on ebay at a AMD 7970 you can pick them up super cheap do to all the miners and its the same as the AMD R9 280. It will save you around $100 and you get alot more performance.

It's the same chipset and more memory; it should work fine.

The actual graphics chip is the same so performance should be identical.