"In every country in the world you've got two or three banks that are simply too big to fail or they'll drive their governments into depression," said Bove.

Apparently Dimon doesn't believe his bank belongs on that list.

"No, we're not too big to fail," he said on Tuesday in front of the House Financial Services Committee, which was investigating J.P. Morgan's recently-disclosed trading losses of at least $2 billion.

Gigantic, But Unlikely to Fail

Of course, just because J.P. Morgan is too big to fail doesn't mean that it will actually fail. Notwithstanding the well-publicized recent trading blunder, the bank has one of the most well-respected management teams and among the highest capital buffers in the industry.

"I don't think the company is likely to fail. But managements change, cycles change," said Bove, who pointed out that J.P. Morgan under former CEO William Harrison was "one of the poorest run banks in the United States."