For the Oracle 12.1 windows client, looking at the output from the TNSPING command seems to work:
With 32 bit installed on 64 bit OS:
C:>tnsping
TNS Ping Utility for 32-bit Windows: Version 12.1.0.2.0 - Production on 02-FEB-2 016 15:44:37
Copyright (c) 1997, 2014, Oracle. All rights reserved.
With 64 bit installed on 64 bit OS:
D:>tnsping
TNS Ping Utility for 64-bit Windows: Version 12.1.0.1.0 - Production on 02-FEB-2 016 16:00:23
Copyright (c) 1997, 2013, Oracle. All rights reserved.