Speaking at the Morningstar Investment Conference today, Ms Davis said European banking was far more concentrated and complex than America.
Problems that concerned US investors were that European banks were more concentrated, more complex, slow to recognise losses, took on too much risk and had poor financial reports.
Ms Davis also questioned the competitiveness as she said smaller banks were regularly set up in America whereas European countries were dominated by two to four retail banks. This meant it was easy to set prices and compete softly between firms.
Indications of unhealthy competition in the banking markets were wholesale funding, increased leverage and rapid credit growth.
Focusing on UK banks, Ms Davis said: "UK banks are not the worst of the lot and in some ways they are very attractive." She then looked particularly at RBS, Lloyds and Barclays.
"I think Lloyds come become a very good bank again, small changes could have a big impact. But we're put off by the PPI debacle, on one hand it's mostly over but on the other hand it was a huge amount of money, this wasn't a small issue and how much of their pre-crisis profit was driven by this inappropriate behaviour?"
On the other hand she said she was "really impressed" with the moves taken by RBS to turn itself around. However, she was more unsure about the moves taken by Barclays chief executive Antony Jenkins to make Barclays the 'go-to bank' and that there was a 25 per cent chance it was only a "cosmetic" change.
She said that some clients were interested in European banks but that she advised them to be cautious.
Firms that were named as possibilities for returns were HSBC, Standard Chartered and Julius Baer which were more capitalised. She also said there was interest in Barclays and BNP Paribas which were reducing risk and offering larger discounts.