Query runs in serial and parallel mode in two identical databases on the same instance
The cost that is determined by the query optimizer is really, a best guess. The guess is based off of CPU/IO resources the optimizer believes that the query will use. If you want to really get some good information (including query costs) install sp_blitzcache - https://github.com/BrentOzarULTD/SQL-Server-First-Responder-Kit