RMAN and export both backup tables, and they both support flashback database, but there are some important differences:
- Data Pump Export (expdp) – The export utility is a “logical” backup, usually done by specifying specific schemas, tables or full.  If you fail to do a “consistent” export, or if you fail to include related tables and use RESTRICTED and CONSISTENT mode (with referential integrity constraints), you may not be able to recover properly.  Export is often used as a supplement to RMAN, usually for the restore of specific tables.
 - Recovery manager (rman) – RMAN is designed for backup and recovery, an extension of the Enterprise Backup Utility (EBU). RMAN takes full, physical, consistent backups of your database files..
 
Advantages & disadvantages of Export:
- Free, and easy to use
 - Very slow, compared to RMAN (examines every data block)
 - Easy restore of a specific table
 - Does not require ARCHIVELOG mode
 
Advantages & disadvantages of RMAN:
- RMAN has block-level media recovery
 - Has a catalog for backup tracking and a report utility
 - Fast – If you dedicate a backup device for each production disk, you can backup terabytes in the time it takes to backup any single disk.
 - Does hot or cold backups
 - Backups and restores can be done in parallel
 - Allows incremental backups (block change tracking)
 - Interfaces with media management systems (TMS)
 
credit: https://www.dba-oracle.com/t_rman_export_expdp.htm