I definitely do my banking on my iPad - even online bill pay on both secured and unsecured wifi networks. It's the same internet whether you're on an iPad of laptop, but the difference is that there are no key logging programs that can run in the background on the iPad like on a laptop or other computer to steal your passwords or credit card numbers when you type them in.
You can even do your banking on an unsecured (open) wifi network as long as the banking site you're dealing with has a secure SSL connection. It's indicated by "https://" at the beginning of the site's URL or a little padlock icon will appear at the top of the Safari window on the iPad/iPhone. Even if you're on an open network, the data you exchange between the banking site and your computer is encrypted, so no need to worry. Just make sure your know what to look for to ensure you have a secure connection.