Q:

Correct or accurate information?

Through a quick Google search, it seems that "accurate information" is more common than "correct information".
When is it better to use correct information?
For example:

Provide people with correct information on this matter.
Provide people with accurate information on this matter.

A:

Correct and Accurate are synonymous. Though 'correct' has a broader meaning. 
For example, consider the following two statements:

Thugs ran away in a car.
Thugs ran away in a blue sedan. 

Both of the above statements provide correct information, but the second statement is more accurate. That's why 'accurate' is more commonly used with 'information'. One can also go for 'precise'. 

