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They have broadly similar meanings. There are cases where only one can be used- we talk about characters in books and films, and we use have + a xxxx personality, not 'character'. We tend to use 'character' when making moral judgments- I wouldn't talk of someone's 'good pesonality', but would say 'good character'.
To me a person with a strong character would be a strong person, who didn't bednd and change-a positive thing. A person with a strong personality could be annoying- loud and excessive, say. A character seems more to do with what's inside the person and personality more to do with how they come across,though there is plenty of grey area in the middle.
Character vs. Personality? 
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