If saving money on interest is more important than paying off something quickly, then pay your credit cards starting with the highest interest rate. Paying off the highest interest rate balance first will take less time and save money on finance charges.
If paying off an account faster is more important than saving money on interest, then pay your credit cards starting with the lowest balance first. When you pay off smaller balances first, you feel more progress since you're knocking out an entire credit card balance.
Exceptions to the Rule
Depending on your credit cards, there may be some exceptions. For example, if you've opted out of an interest rate increase and your credit card will be closing soon, you should pay off the balance quickly to keep from hurting your credit score.
Is One Method Quicker?
When it comes to the time required to pay off your credit card balances, there isn't a huge difference in the two methods. In the end, you don't have to choose either of those two. You can pay off your credit cards in whatever order makes you happy - you can alphabetize them by credit card issuer. The goal is to pay off your credit card balances by making a lump-sum payment to one credit card each month until that balance is repaid. Be sure to make minimum payments on all your other credit cards.