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You can apply for both cards and use them together for different travel expenses. But if you need to choose one, think of what you are going to use the miles for. The Citi Premier® Card is a part of the ThankYou Rewards program and earns ThankYou points on all purchases. ThankYou points can be used to cover travel expenses like airfare, hotel stays, rental cars or cruises. Also, if you need to fly with an airline other than Lufthansa and its partners, this credit card will come in handy, because bonus miles can be redeemed with any airline. The Miles & More® Premier World MasterCard® is good for redeeming miles at particular airlines (Lufthansa and its partners) as this way you will use miles at their full potential.