If your ODBC application is running 32-bit mode (even if the server is running 64-bit AIX kernel) you would use a 32-bit driver; if your application is 64-bit, use the 64-bit version of the driver. Both are available for AIX.
I am planning to install a third-party application which product specification said that it only support ODBC driver for Teradata on 32-bit mode. On the other hand, my box currently comes with AIX 5.3 64-bit.
I read from release notes of ODBC Driver For Teradata Version: 13.00.00.00 can support both AIX 32-bit and 64-bit.
There are two separate drivers, one that can be called by applications running in 32-bit mode and one that can be called by applications running in 64-bit mode. Starting with TTU13.0, they are packaged together in a single install. In prior versions, they are separately packaged and you can install either one or both. Just be sure your application references the correct paths in LIBPATH, .ini files, etc.