The overall efficiency of photosynthetic energy conversion depends both on photochemical and excitation energy transfer processes from extended light-harvesting antenna networks. Understanding the trade-offs between increase in the antenna cross section and bandwidth and photochemical conversion efficiency is of central importance both from a biological perspective and for the design of biomimetic artificial photosynthetic complexes. Here, we employ two-dimensional electronic spectroscopy to spectrally resolve the excitation energy transfer dynamics and directly correlate them with the initial site of excitation in photosystem I-light harvesting complex I (PSI-LHCI) supercomplex of land plants, which has both a large antenna dimension and a wide optical bandwidth extending to energies lower than the peak of the reaction center chlorophylls. Upon preferential excitation of the low-energy chlorophylls (red forms), the average relaxation time in the bulk supercomplex increases by a factor of 2-3 with respect to unselective excitation at higher photon energies. This slowdown is interpreted in terms of an excitation energy transfer limitation from low-energy chlorophyll forms in the PSI-LHCI. These results aid in defining the optimum balance between the extension of the antenna bandwidth to the near-infrared region, which increases light-harvesting capacity, and high photoconversion quantum efficiency.