LiMPO4(M = Mn, Fe) olivine phosphates are important materials for battery applications due to their stability, safety, and reliable recharge cycle. Despite continuous experimental and computational investigations, several aspects of these materials remain challenging, including conductivity dimensionality and how it maps onto Li pathways. In this work, we use a refined version of our finite temperature molecular dynamics "shooting" approach, originally designed to enhance Li hopping probability. We perform a comparative analysis of ion mobility in both materials, focused on many-particle effects. Therein, we identify main  diffusion channels, as well as means of interchannel couplings, in the form of Li lateral  hopping, which markedly impact the overall mobility efficiency as measured by self-diffusion coefficients. This clearly supports the need of many-particle approaches for reliable mechanistic investigations and for battery materials benchmarking due to the complex nature of the diffusion and transport mechanisms.