The Verdict
Here's the recap:

1. Citibank: Call-center rep did not seem to understand my questions and tried to refer me to the website for answers.
2. Chase: Call-center rep didn't offer clear explanations but kept trying to get me to sign up anyway.
3. Bank of America: Call-center rep understood my questions, explained customer-facing security mechanisms and offered advice about how I could protect myself.

After the calls, I rang Larry Freed, president of the research group ForeSee Results, to see what he thought. Freed is a former banking CTO who does a regular survey on banking customer satisfaction in conjunction with Forbes.com. He has told me in the past that customers who have not signed up for online banking often cite security as a factor.

Online banking is a huge area of growth for banks—if they can get it right. According to Freed's latest survey, customers who are not doing online banking report an overall satisfaction level of 70 on a scale of 0 to 100. For those who do online banking and bill pay, the satisfaction level jumps to 79. What's more, those who are doing online banking and bill pay are much more likely to purchase additional services from the bank—59 percent likely, rather than 36 percent.

Nevertheless, Freed didnt seem surprised that the banks, for the most part, had so little to say about online security. "The education and communication of security is not done very well," he said. "For converting non-online banking customers, I think that's a critical step. But it's a balance between putting the fear in them and educating them."

Right now, I'd say, the banks are doing neither.

As for me, if I had a Bank of America account already, I think I'd give online banking a try. It's not so much that I'm convinced Bank of America actually has better security than Citibank or Chase. The call-center rep doesn't know that, and none of the banks are going to talk about all their security mechanisms anyway. But I'm heartened that they're teaching their call-center reps how to explain their security mechanisms to customers. At this point in history, it's a sad fact that merely being willing and able to talk about security in plain English (even if they don't want the call to be recorded) puts Bank of America well ahead of its competitors. That's just not enough to make me change banks, though. Guess I'll keep buying stamps after all.