The syslog database is actually composed of three data spaces. The data space files can be found under NMSROOT/databases/rmeng. However, purging does not shrink the size of these files. The only way to shrink them is to completely remove them, and rebuild fresh data spaces. There is a class file, DBSpaceReclaimer.class, available from the TAC that can do this.
The SyslogPurgedDataBackup* files are text copies of the data that is purged from the syslog data spaces. These can be kept to preserve an extensive audit trail (useful for various compliance standards). You can configure the syslog backup settings under RME > Admin > Syslog > Set Backup Policy.