Dressing nicely is sufficient - the majority of the people that attend tumor boards at my school do not think of it as such a special occasian as a medical student. It is a bunch of people that are coming from lab, clinic, etc. and some are dressed in plain clothes or lab coats or scrubs. It's a hodgepodge, but for my first tumor boards I wore my white coat getup and felt overdressed for the occasion.
When I asked my PI she said a white coat wasn't necessary but in the end being overdressed is better than being underdressed and your PIs opinion is what matters.