Hi,
A platform upgrade is a back end upgrade. If you receive this upgrade there are no changes you need to make in order for your model/reports to work. It is usually a release that fixes bugs or enhancing the platform in some way. If you have made customization's to your model or reports you can still get a platform upgrade.
A content upgrade can be applied to each individual component within Apptio. This means you can apply it to a specific component of your choosing or to all. Content upgrades provide you with new/improved reporting capability or new/improved model logic etc. If you make customization's to the OOTB configuration of the model and reports within Apptio the content upgrade path may be broken. This means you will have to revert all your work back to stock in order to receive the new updates and you will need to redo your customization's.
Please let me know if you want more information or any clarification,
Lauren Griessel