Both countries (Malta and Cyprus) allow their citizens to have citizenship of different states. You can obtain citizenship of Malta and Cyprus if you wish. There are no special privileges. Cyprus is not a member of the Schengen Zone.
How can I apply for Cyprus citizenship if I have another EU passport?
If I have another EU citizenship – from Bulgaria, Portugal or Malta, for example – can I still apply for Cyprus citizenship through a citizenship-by-investment route? Is there some special process? What would be the benefit of me being a Cyprus citizen if already an EU citizen?