One worry i'd have about using google sites would be security, if these project sites aren't necessarily meant to be public. Although that argument assumes Business Catalyst is secure. I don't know.
But, between the two, google locks you entirely into their format and at least sites built in BC have some (semblance) of freedom in terms of what users can create. Web apps are a bit tricky in terms of portability but that basic functionality could still be replicated elsewhere.
