* Many PaaS offerings (like AppFog) are not like shared hosting at all, only the free offering hosts people multi-tenant, when you pay you get dedicated VMs
* The platform in platform-as-a-service means it connects you to fully managed services (on Heroku there are all the add-ons as well as Postgres, on AppFog there are add-ons and MySQL).
* One of the most compelling parts of PaaS is that it is managed by someone else so that you don't get a call at 3am when it is broken
Moreover, if you were to run a PaaS on your own, it would make more sense to try Cloud Foundry which has specifically addressed at least the services aspect of the above comments.