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
This is a matter of what kind of concerns you want to have in the application:
I would pick the one I am best at, as Kevin said above.
Edit
More about Kevins post: you can also have your application under sharepoint but with full access to the API, in my projects we do it as a normal ASP.NET application, with own masterpages and everything, but we still use the authentication, lists and doc libraries for uploads, roleassignments for permissions etc. Its a very viable hybrid.