I think your best bet, if you are intending to actually copy the entire physical SQL Server Express database from one server to another, is to do this using RDBMS tools. Alternatively, if you have an empty SQL Server Express database that already exists on another server and you're looking to simply import your GIS data, just make sure it contains the SDE tables and then use either a GP tool or a manual copy/paste from ArcCatalog. The Import, Feature Class to Feature Class, or Feature Class to Geodatabase tools are all potential solutions depending on what you are trying to achieve.