Finite element simulations are presented, showing material utilisation and electrochemical cell behaviour of a rechargeable Li-ion microbattery in planar thin-film, 3D and 3D core core-shell nanoarchitectures in which the active material is 250 nm thick as a shell on a 250 nm diameter core support. The materials simulated are non-porous additive-free LiCoO2, lithium metal and solid-state, polymer, polymer-gel and liquid electrolytes. The concentration profile of the LiCoO2 during discharge and areal energy versus areal power in a Ragone plot for each of the different architectures are compared. It is shown that the planar thin-film architecture gave better cell performance when used with the solid-state electrolyte with all three architectures showing material utilisation of the cathode at the closest point to the anode. The 3D and 3D core-shell nanoarchitectures show better battery performance for the polymer electrolyte then the planar thin film, with the 3D nanoarchitecture being the best. The 3D core-shell architecture shows a significant improvement in performance by comparison with the thin-film and 3D nanoarchitectures when a polymer-gel or a liquid electrolyte are used. The 3D nanoarchitecture shows a slight decline in performance when going from a polymer-gel electrolyte to a liquid electrolyte with faster Li-ion transport. The 3D core-shell nanoarchitecture shows improved cell performance with faster Li-ion transport. The adoption of 3D nanoarchitectures with suitable electrolytes can have a significant improvement in battery areal energy and power performance.