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I agree with Miriam, without further details, it is really hard to say what is going on. However, depending on where you are actually searching from does factor into the results as well as the website associated with the listing. Additionally, the number of citations a location has and how well those citations match up, meaning name, address, and phone are all exactly the same, can influence local listing rankings as well. Whether or not the competitor has claimed their listing isn't really a huge factor in determining rankings. The fact that your competitors website outranks yours is an indication as to why those local listings may appear to be more relevant to the search, and therefore rank higher, than yours.