The average time of your credit cards being open is one factor. If you close an old one you will take a small hit, less than 20 points I would imagine depending on your overall score.
It makes no different if you use THAT card or not.
What matters is the % of available credit used. Example, if you carry a balance of 2500 each on 2 cards with a limit of 5000 each, that's the same as a balance of 5000 on 1 card with a 10000 limit. Both situations are 50% credit utilization.