If there are more records in the new copy of the database update existing records should work for you. New Record 1 will replace Old Record 1. New Record 2 will replace Old Record 2, etc. No matching is occurring on the records, so if a record was deleted in the New data the following record from the New data will now overwrite the Old data.
More here: http://www.filemaker.com/help/html/import_export.16.10.html
The other way to overwrite everything is to simply Delete All Records and then import with Add New Records.
You'll want to think about any automatically-generated indexes that the records have to make certain that you are doing the right thing. A few practice migrations will really help clarify what needs to be done. Even better, you may be able to script the data migration after you've done it by hand once or twice.