Minecraft just released today for the Xbox One and PS4. You can pick up the title for $20, or if you already owned it on your previous gen console, you can get it for only $5. Here's a quick comparison of Minecraft on the Xbox One vs. the Xbox 360 version, and also a simple tutorial on how to transfer your Xbox 360 saves to the Xbox One. This same comparison can most likely be used for the PS3 vs PS4 versions as well. Enjoy!
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There really aren't any noticeable graphics differences between the two versions, but one thing you may notice is that Minecraft on the Xbox One has a much better soundtrack, and is quite a bit larger than the Xbox 360's version. About 32x larger in fact. You may also notice the Xbox One edition has a slightly longer draw distance, meaning you can see objects further off in the distance.
One thing to note is that when using one of your Minecraft: Xbox 360 saves on the Xbox One version, the two will be identical in size. The only time the world will be larger on the Xbox One is when you're creating new worlds.
So, if you've owned the previous version, and just want to expand upon what you've already created, then there may not be any real point in upgrading to the new version on the Xbox One unless you just don't use your old console. However, if you're deciding between the two, well, Minecraft on the Xbox One will definitely be the better version of the two.