The dissimilar lattice-evolution of the isostructural layered Li(Ni,Co,Al)O2 (NCR) and Li(Ni,Co,Mn)O2 (CGR) cathodes in commercial lithium-ion batteries during overcharging/discharging was examined using operando neutron powder-diffraction. The stacking axis (c parameter) of both cathodes expands on initial lithiation and contracts on further lithiation. Although both the initial increase and later decrease are smaller for the CGR cathode, the overall change between battery charged and discharged states of the c parameter is larger for the CGR (1.29%) than for the NCR cathode (0.33%). We find these differences are correlated to the transition metal to oxygen bond (as measured through the oxygen positional-parameter) which is specific to the different cathode chemistries. Finally, we note the formation of and suggest a model for a LiCx intermediate between graphite and LiC12 in the anode of both batteries.