What's the difference between 之间 and 中间?
I think there's a couple more important distinctions. 

中间 is used for when talking about the physical location being in the center/between.

ie. You would say:


  箱子的中间有个人。


之间 is used when abstract things are in the center/between. This applies to things like numbers.

ie. You would say:


  我们之间没有爱。


Here's a specific example of how the two words have a different meaning.

我们中间有障碍。 : There are (physical) obstacles between us.

我们之间有障碍。 : There are (mental) obstacles between us.