We are starting a new project to deploy a solution in cloud with the possibility to be used for 2.000+ clients. Each of this clients will use several tables to store their information (our model has about 500+ tables but there's less than 100 core table with heavy use). Also the projected ammout of information per client could be from small (few hundreds tuples/MB) to huge (few millions tuples/GB).
One of the many questions we have is about performance of the db if we work with only one (using a ClientID to separete de clients info) or thousands of separate dbs. The management of the dbs is not a huge concert as we have an automated tool.
More details would be helpful, some of which could include: how much memory is dedicated to Postgresql, how many servers, are you using replication/hot standby, what are you data access patterns like (mostly inserts/lots of concurrent queries, a handful of users versus hundreds querying at the same time), what are your plans for backups, what are you planning to do to archive older data?
Also, have you considered separate schemas rather than separate databases?