Yes BAPI is efficient than BDC.
The BAPI and BDC are actually meant for different pruposes.
BAPI are developed for webservices in which the calling 
application can directly call the BAPI and carry out the 
required operations, where as in BDC we have to write a 
code and then we need to get the data in SAP system in a 
perticular format and validate the same and then carry out 
the updation or other operations, in case of BAPI is a 
business object repository object which can be called from 
any application. where as for BDC program we need to get 
the input file and execute it manually or as a batch job.

Many of us face probelms in upgradation projects for BDC 
programs as the screen sequance of some other settings gets 
changed so we need to redo the coding(recording) of BDC and 
for some transactions its not possible to record as well 
such a enjoy transactions, in these cases BAPI is a very 
good and proper alternative.