When you consider which frequent flier credit card program is best, ask yourself two questions: Will I be able to get benefits from the dominant airline(s) in my region? Which one will earn the quickest ticket with the fewest strings attached?
Airline sponsored credit cards allow you to focus on a single airline. If that airline has a hub in your city (or nearby), it may control most of the routes to potential destinations. This will make it convenient, efficient, and therefore economical in many cases.
Bank Sponsored credit cards allow more flexibility, because the miles earned can be used on many airlines rather than just one. If you don't have a dominant airline in your region, these cards probably are your best bet. They have other advantages, too: sometimes the minimum mileage required for travel is lower than with airline-sponsored cards. But these cards usually come with more fine print, too.