Exciton-vibrational coupling in molecular aggregates: Electronic versus vibronic dimer

► The effects of exciton-vibrational coupling have been considered in two dimer models. ► A complex behavior of the energetics in the vibronic dimer has been found. ► Dissipative dynamics of two models is investigated using Redfield relaxation theory. ► Explicitly accounting for vibrational levels can significantly change the dynamics. ► A transient population trapping is found in the one-exciton excited states.