Ultrafast excitation relaxation within a manifold exciton state and long-lived vibrational coherence are two universal characteristics of photosynthetic antenna complexes. In this work, we studied the two-dimensional electronic spectra of two core light-harvesting (LH1) complexes of Thermochromatium (Tch.) tepidum, native Ca2+-LH1 and modified Ba2+-LH1. The role of the vibrational coherence in the exciton relaxation was revealed by comparing the two LH1 with similar structures but different electronic properties and by the evolution of the exciton and vibrational coherence as a function of temperature.