With seemingly growing identity and card fraud activity in the world, it is wise to select debit cards with solid security features. A few of the important features in my mind are $0 liability if the card is ever stolen and unauthorized purchases are made, automatic fraud early warning systems or monitoring (make sure it is included at no extra cost), and a prompt and friendly security department to assist with card replacements and replenishment of cash if the need arises.
Due to intense competition among financial institutions and a general consumer concern for privacy and financial security measures, most that offer debit cards will also provide these key features. It is still wise to ensure that the institutions do provide them and to learn about any other additional features you may be interested in. For example, I recently read that one bank offers a temporary card number for online purchases, making it virtually impossible for anyone to steal the real card number.
Some differences between cards may relate to the promptness in their response to your inquiry, how fast cards are replaced or cash supplied while a card is being replaced, how the fraud is monitored and how you are warned of potential fraud and finally what the level of service is from the security department. You might consider asking trusted friends or advisors if there are any particular institutions they have had experience with and whether or not they would recommend the security features provided with their respective cards.