Currently? Of course not. But when the idea of storing money on your computer (e.g. in a file) becomes more widespread, then the answer would be yes. Or at the very least it would be equally secure.
It's not that hard to provide people with a secure environment, as long as that environment is designed with with security in mind. A non-jailbroken smartphone is probably good enough, though a dedicated device might be better. And you can use live boots.
I can see a future where we use such (or similar) things to do money transfers.
Wells Fargo is a bigger target, but they also have many more layers of protections and an interest in providing customer service. My hunch would be that it would be easier for a criminal to profit off of attacking WF than attacking a personal bitcoin user, but that it would be easier to actually cause financial harm to a personal bitcoin user (even without profiting themselves). But to clarify that, I have a couple of questions about how storing your own bitcoins works, since I've never used it:
* How does bitcoin storage work with offsite backups? If someone compromised the backup, would that give them access to your money?
* If you lose the file (hard drive crash, home burns down, backup system fails, whatever), does neither you nor anyone else have that money anymore? I.e., someone wouldn't have to gain access to the money themselves to deprive you of it?
keep your wallet file encrypted and back it up to multiple locations on a regular basis (to update the backups with new private keys that are created by your client software).
there are also ways of generating bitcoin keys completely offline as well as producing signed valid bitcoin transactions completely offline. This way you can forward funds to keys that are not on a machine connected to the internet, or keys that are backed up only on paper (in multiple safety deposit boxes if you like). And also you can then put signed transactions from the offline machine onto a usb stick or whatever and then use a networked machine to forward those valid transactions to the bitcoin network.
Coinbase is doing something like this for their storage of customer funds. Coinbase seeks to be a bitcoin bank that wont get hacked or that if it somehow does get hacked (cough inside job, cough) that only very small losses could occur.