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
Welcome to the dark land of politics.
It's worth making sure that your team properly evaluate and understand any compromises that SharePoint will have you make. Asking here is a good start. Things I'd look at include:
What's the whole solution going to include? Often the administration of a site can involve as much or more development work as the front end. While the 3M+ user front end is the glamorous part it may not be the bulk of the work.
Are there reference sites for 20K+ simultaneous user SharePoint sites? Honestly? What kind of hardware did that require? Is that available?
Get a small group of experienced contractors in for a few weeks to properly estimate the work, both on ASP.NET MVC and SharePoint. Make sure they've worked on large sites. (There's plenty of contractors around at the moment!)
Also, anticipate failure. Have a fall-back option:
If the MVC technologists win out, expect heat from senior management, and possibly even a skunk-works we'll-do-it-properly-anyway project that duplicates your efforts.
If you do end up with SharePoint, listen very carefully to users throughout the development process and be prepared to create Web parts, MVC pages or whathaveyou to address problem points.
I've been in a similar situation where it turned out that there was heavy vendor influence at a very senior level. The senior team had bought into SharePoint and required it to be used for all internal systems; the OCTO (Office of the Chief Technologist) had mandated open-source technologies. It was fun to watch the fur fly in the middle.
(Our option in the end was to use a service-based architecture based on REST, which effectively booted the current version of SharePoint out of the system altogether.)