BDC is the BAtch Data Communication is the process of 
transferring data from a SAP system to an SAP system or 
from a non-SAP system to an SAP system.

Lsmw or Legacy System Migration Workbench has the same 
purpose but it is basically a tool to upload data. It 
offers several method like batch input recording, IDOC, 
Bapi, direct input,  while BDC uploads data using batch 
input recording.

 Lsmw is a built-in tool provided by SAP and we do not need 
to write lines of code to upload data but we ned to merely 
configure the Lsmw tool. first we have to choose the 
appropriate method in LSMW , then the tool will act like an 
wizard and all steps will be shown one after another in a 
structured manner.and we have to just proceed in the shown 
manner and have to do or configure in some of the steps. 
but in BDC we do not enjoy such.
So BDC will be mostly used by ABAP programmers and LSMW can 
be used by functional consultants easily.
  BDC will be used for less data upload and LSMW for a 
large no of data transfer in a less time.In BDC using 
session method we can not upload more than 999 records in a 
single session.But in LSMW we can upload near 5000 data 
records.

  BDC is mostly used for customized data upload. suppose if 
we use direct upload in LSMW then we have to use the 
standard business object to upload data, but for customized 
data We will find no BAPI. So we can use BDC.