bapi's are procedural and object oriented .

the main advantage of bapi's is they are also used for the
migration of data from one non-sap to sap system.

bapi's are useful for certain taransactions where bdc's
can't be used like nace transactions.

1.bapi's are always backword compatible i.e which can work 
on upgradations also.
2.bdc will not work for upgradations.
3.bapi provides versions for each and every upgradations.

BAPI:

Bapi's are procedural and object oriented .
Bapi's are used for Njoy transactions also.
Bapi's does not support recording.


BDC :

Bdc is not used for Njoy transactions.
Bdc support the recording.