A mobile phone is completely different to the Internet (as it is accessed via a PC). The difference is in terms of the charateristics of the device, the behaviour of the people using it and when and where and by whom it is being used. It is important to consider all of these factors when developing mobile banking solutions.
A mobile phone is different because of a smaller screen, a different keyboard and no (or sometimes an akward) pointing device. So when designing software for mobile phones, one must take these constraints into considerations. Solutions with a lot and superfloues input will not be successful. Many different keystrokes and inputs for exceptions is not a good idea. It is much better to try and deduce values than to expect entry for every value. (For instance, we assume that one primary bank account is associated with one mobile phone and does not require a client to enter a bank account every-time. Not only is it easier to input, but actually more secure - if you think about it).
Another thing to consider is when and why people would want to use mobile phones. Where the Internet works well to browse and to collect a lot of information (for instance when you want to perform a share trade and graphs and information about previous transactions are important - it is probably more suitable to perform these transactions via the Internet). On the other hand people tend to use mobile phones to do a specific transaction only (send a text or make a phone call). Banking transactions in this mould is therefor ideal candidates for mobile banking. (We tend to offer different types of payments of the ability to purchase stuff as typical banking features on mobile phones).
Also consider the typical mobile banking customer. This person often don't have access to the Internet, is very capable in using the mobile phone, but is also time and cost sensitive. It is important to design banking transactions with these customers in mind. Easy to use, low cost, yet powerful and quick transactions are typical candidates.