The best replacement for bapi is bdc.

The best alternatives to bapi are rated as following:
★★★★★  bdc
★★★★★  idoc
★★★★  rfc
★★  badi
★★  function module
★  rfc abap
★  abap
★  rfc sap
★  idoc sap
★  ale
★  bdc abap

Your alternative for bapi is not listed? Suggest!
Speaking about bapi, one probably shouldn't forget about lsmw.

Other search terms related to bapi and their ratings are:
★★★★★ lsmw
You have in mind a companion for bapi and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of bapi in all years. Click on graph for more.
bapi
bdc
idoc