libpq is generally-speaking better than psqlodbc. The advantage of ODBC is that if you have a suitable driver, you can connect to other DBMS' as well, while libpq will only work with PostgreSQL. Unless you need such portability, go with libpq.
Thanks everyone for sharing comments, really useful ones. Yes the requirement is not connecting to other DBMS but only Postgres and libpq is the correct way so far from comments here. Regarding libpq performance wanted to discuss about connection polling like pgpool but I think a separate post of performance will make sense.
So, coming back to the original question actually I am exploring on both fronts here - libpq and psqlODBC. Just one thought here, there is an existing ODBC business logic code which is talking to sybase database and now same code need to be ported to talk to postgres, then in this case will the use of psqlODBC quick way? Otherwise porting of ODBC business logic to libpq constructs needs to be done.