I will second what jailbait said. I also doubt there are any significant differences in the security features amongst major Linux distros.
I would recommend running a software firewall and some kind of "no script" type add-on in your browser, if one is available, if nothing else to cut down on the clutter. I use "notscript" in Opera and "noscript" in Firefox. You will then need to turn on the scripts that your bank's website will need to function; it's a little extra work up front but the long-term benefits, both in the control and in knowing how the heck many pointless scripts many websites run, are worth it.
I also delete new cookies on exit from the browser, but that has more to do with getting rid of long-term tracking cookies than with banking.
I also do not use browser-based password storage--I use KeePassX
(based on a friend's experience with KeePassX on Windows, I would recommend avoiding the beta version at this time).