This calculator shows the tradeoff in holding a no-annual fee card with a higher interest rate versus an annual fee card with a lower rate. You can also enter any introductory "teaser" rates and the period offered.
Your decision depends, in large part, on your card use. If you pay off your balances promptly, you don't incur any card interest expense. There's little reason to pay an annual fee for the privilege of paying the card company promptly.
If you tend to carry a card balance, you should aim to minimize interest expenses by using a low-interest rate card. You may have to pay an annual fee in exchange for the low rate but may save more in interest expense during the year than the cost of the annual fee.