In general, Apple and Android tablets are safer to use on the Internet than Windows or Apple Mac computers. This is because only software from the Apple or Android stores can be installed. All apps in these stores are vetted and checked for malware. With a Windows or Mac computer, software from anywhere can be installed either by the user or by an exploit on a website. This dramatically reduces the risk of malware (trojans, viruses etc) but doesn’t stop phishing (conning the user into divulging sensitive info like passwords, dates of birthday, mother’s maiden names etc)
In January 2014, a (very technical) report was published which showed big security holes in banking apps for the iOS (iPad, iPhone etc.)
A genuine secure page for a bank will be digitally signed from a trusted source – however, a malicious person can create self-signed pages too. If you visit those pages with a regular browser, like Firefox, Internet Explorer, Chrome or Safari; you get a warning but with 40% of the apps tested, there was no warning. So you could be typing your user name and password into a fake page. Then, the owner of the page could use those details for their own ends.
So, the best solution is to use the browser on the tablet, and if you get a warning, get the hell out of there!