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
The problem with asking whether Sharepoint is easy to customize is that there's a wide range of levels of customization people are experienced with. And for some reason, most people also seem to think that whatever level they customized Sharepoint to is the extent to which anyone else would also try to customize Sharepoint.
It's hard to talk about degrees of customization in concrete terms. What is "customization" to me is wrangling with the core DAL, fighting with bugs in the CAML to SQL query optimizers, overriding the SPListItem hydration pipeline, etc. To others, "customization" might mean building some web part widgets and deploying them in a WSP. If you find that there is some impedance mismatch between your logical model and Sharepoint's working model, you will have a really hard time reconciling the two.