First off all, online transactional system should be standarts compilant, which means no matter which browser you use it just works.
Dunno about USA but in Poland there are banks where transactional system works only for IE, some even force you to install a separate certificate, so you are able to use that online system only from one computer*, pretty useless as for ONLINE account, some even require to sign with your own blood
[*] unless you install that certicicate into Windows on VirtualBox and keep that image with you on the flash pendrive.