Some better-designed apps are more in tune with the fact you are accessing the service with a mobile phone. For example, if you are in another city, away from your bank, the app can give you suggestions on where to withdraw money from an ATM with no fee by using your bank's partner network.

"You don't even need to know your ZIP code," Bissell says. "That's one of the nice things you can do when you have an app for your bank."

Some bank card apps even give you what's called "location-based services" with advice on hotels or restaurants with the best deals, and even coupons, says IBM's Hissam.

"There's a lot of convenience factors … and can include loyalty points and more," he says.

Applications also are combining mobile banking with near-field communication, or NFC -- a wireless communication technology that uses short-distance radio waves to transmit data -- to allow you to pay for services or products at the point of sale. Google Wallet and MasterCard PayPass are examples of this type of payment capability.

Some mobile banking applications allow you to take pictures of payroll or other checks written out to you and then digitally transfer the amount of the check into your account.