Question: What is the difference between *quite* and *pretty* in the following context:

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> The differences between these concepts are quite complicated.
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and

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> The differences between these concepts are pretty complicated.
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Answer: 
*Pretty complicated* is approximately the same as *fairly complicated*: there is a significant degree of complication. It is complicated enough that it will require much effort for an ordinary person to understand it.

* *Pretty*, in this sense, is used mostly in conversation, very little in formal discourse.

*Quite complicated* is more complicated than that: *very complicated*. It is so complicated that an ordinary person may not be able to understand it entirely. 

* *Quite* is used mostly in formal discourse, much less in ordinary conversation.
The usage of the word "quite" in modern English is a paradox. It can mean two opposite things:

The original meaning is still used sometimes:

"He is quite dead." (You cannot be slightly dead, so "quite" in this context means, "absolutely.")

The modern meaning can mean anything from "moderately" through to "surprisingly."

"They said I'd hate Javanese cooking but I found it quite tasty."

In this second context, the word, "quite tasty" could be substituted by the word "pretty tasty" and it would mean the same thing.