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The Bank of America iPhone app is a direct port of their iPhone web app. No extra bells and whistles have been added. The only major difference that occurs is that when you select a link to follow, you won't have to see all the work Safari would be doing to load the next page.
While there isn't much more functionality that needs to be added to the mobile banking solution for Bank of America, it seems awkward that they would choose not to take advantage of a native iPhone apps capabilities.
All of your account information is still presented in the same fashion that it is on the mobile app. That means that you're still reading straight text on a white screen. On the regular web version of their site, the information is displayed to you in a very neat and easy to follow manner. This app could have easily reformatted the information to follow that styling and made everything much more appealing.
Nothing is lost in the transition to native app, but nothing is gained at the same time. It's not as if you can view the information for your account without being able to access the internet, so there really isn't any benefit over having a bookmark icon to the web app. If you have Bank of America, you'll probably download this app and simply enjoy it for providing you with the information you need. But if you don't, this isn't going to convince you to go sign up for a new account or anything special like that.