There are some minor variations--for example, in the benefits for dependent children of contributors, and so on--but basically the two plans are the same. Quebec's plan is administered in Quebec. The CPP is a federal-provincial thing, and in fact Quebec has a vote on changes to the CPP.
If you are somebody who works both in Quebec and in some other province, or if you have worked in Quebec in the past and then you work in some other province in Canada, your pension at the end will be based on a combination of both plans. Your service in the QPP would be combined with what you had in the CPP, so your pension would be based on a combination of the two.