As a continuation of our earlier work [J. Phys. Chem. A 123, 5491 (2019)] we investigate the excitation energy transfer for the 2-aminopyridine dimer, (2AP), and the 2-pyridone.6-methyl-2-pyridone (2PY.6Me2PY) heterodimer by using basic exciton theory and the Fulton-Gouterman (FG) model Hamiltonian. The inclusion of the monomer vibrations and the bias (or ) restrict the population transfer and lead to partial localisation of the excitation. For the homodimer, the time-period of the population transfer and also population exchange obtained from the FG formalism is well reproduced by simple exciton theory when using the quenched excitonic splitting. On the other hand, the comparison is not so good for the heterodimer where a bias is present.