One connection vs multi connection
In postgreSQL, database is a logical concept and a PostgreSQL server manages one database-cluster which contains all databases.
The number of databases does not affect to the server performance.

I recommend that you divide databases at the viewpoint of logical structure. If your system can be completely divided into each mini site, you may create databases corresponding to the sites. (When the access of one site increases, you can divide and relocate the site to  other server.)