The new, Laplace transform based multi-state local CC2 response method is compared to the previous single-state approach. The new method employs adaptive state specific local approximations for the eigenvectors of the Jacobian. As a result, it is much less dependent on the initial un-truncated CCS wavefunction and able to locate the relevant eigenstates also in difficult cases where the initial CCS eigenvectors are qualitatively wrong and where the original single-state method failed. In this paper we compare excitation energies, transition strengths, and dipole moments of the individual local approaches and the canonical reference calculation, for a set of different molecules and excited states.