I might be missing many factors here but using the same postgress process is probably better option. There are many examples for storing metadata in frameworks like spring. etc. For example Jira is using single database but creating namespaces for the plugins and setting up permissions for them, so the plugin is not going to mess up the core database (has read only access).

TL;DR - Aproach nr2 is IMHO magnitude better, but we could also use some other mechanisms for separation like namespace:
https://www.postgresql.org/docs/9.3/static/catalog-pg-namespace.html