IMO, it isn't an either/or decision. Try to strike a balance between both.

In general, credit card debt is the worst kind, and by paying it down you start saving lots of money on interest. A couple of things that you could consider if the budget will allow it:

1) try to pay off all new credit card charges in full when the bill comes in (don't add to the debt). Or, use cash.

2) Always try to pay more than the minimum amount due, even if it is only a dollar. Then try to keep paying down the remainder using a fixed amount that is in the budget, but always exceeds the minimum payment. The amount you own will go down, interest due will go down and more of what you pay will go into paying off the debt.

3) in this economy, almost everyone has already done it, but really really scrub your budget, especially for those items with the "low monthly payments" --- they can be like a cancer in your budget.

4)Also, find alternatives to just following the crowd. An example: all of the library's around here lend DVD's and CDs--why rent movies or buy music when you can borrow? Small savings add up. Or, "brown bag" lunch. The folks at work who go out every day spend 5 or more dollars a day; call it 25 per week, or 100 a month. I brown bag for about 1-2 $ per day; call it 20-40 per month, saving 50 or 60 a month. We all have better things to do with our $$.

5) If you have a good record with the credit card company, call customer service and ask if they will lower your interest rate, if they ask why, just say you think it is too high for your good record. You will be amazed at how often they can lower the rate; they will not offer to do it, but often can and will if asked.

These are just ideas we have found useful. Good Luck.