Hi Jenny,
I see nobody has made a specific comment on your question yet, apologies for that. Comparison of Private Cloud vs Public Cloud is generally achieved by defining these as server characteristics under the "Virtualization Profile" column in Server Master Data. When Business Insights is activated, comparison of these profiles will then be populated as part of the OOTB report content included with the Server Optimization component.
Assuming your Apptio contact has given you instructions on how to see the Apptio Reference Project, you should be able to open the reference project, and navigate to the sample report for this under the "Server - analyze spend & usage" button.
Hope this helps!
Regards, Ian.