This work treats the impact of vibrational coherence on the quantum efficiency of a dissipative electronic wave packet in the vicinity of a conical intersection by monitoring the time-dependent wave packet projection onto the tuning and the coupling mode. The vibrational coherence of the wave packet is tuned by varying the strength of the dissipative vibrational coupling of the tuning and the coupling modes to their thermal baths. We observe that the most coherent wave packet yields a quantum efficiency of 93%, but with a large transfer time constant. The quantum yield is dramatically decreased to 50% for a strongly damped incoherent wave packet, but the associated transfer time of the strongly localized wave packet is short. In addition, we find for the strongly damped wave packet that the transfer occurs via tunneling of the wave packet between the potential energy surfaces before the seam of the conical intersection is reached and a direct passage takes over. Our results provide direct evidence that vibrational coherence of the electronic wave packet is a decisive factor which determines the dynamical behavior of a wave packet in the vicinity of the conical intersection.