is safer than managing it by phone, certainly. When you are online to your bank you are connected via a secure session that is 128bit encrypted. If all the registered members of this forum sat down with electronic calculators and worked 24 hours a day for the rest of their lives they would not succeed in cracking that level of encryption.
The danger lies in keeping records of your username/password combination and your account number(s) on your hard drive. That's a very foolish thing to do, and if they're compromised you can hardly blame the online banking system.