We need to develop quite a powerful web application for an investment bank. The bank IT would like us to build it on top of the SharePoint platform
SharePoint development can be tedious but I'd hardly say the platform cannot be easily customized. I recently began developing with it full time and so far, I impressed at it's flexibility and suitability for my application but my needs are quite different from what you've described.
I understand 2007 is a vast improvement over 2003 so perhaps your information is only outdated. I hear 2010 is going to again be a significant improvement.
It's your job to deliver the functionality that the customer desires. If they desire a SharePoint solution, unless there's some particular reason why SharePoint really is a weaker model, that's what you should be able to deliver. In the event that SharePoint isn't a good fit, you need to be able to explain why to the bank's satisfaction. I'm not convinced "We don't know SharePoint" is an acceptable response in this situation: the bank's inclination should, at that point, be to find someone who knows both technologies well enough to deliver a product in SharePoint or better explain why SharePoint isn't actually what they want.