We focus on comparing the performance of two tunnel manganese oxides with square tunnel structures, α-MnO2 (K0.11MnO2), which contains tunnels of 2x2 octahedra dimension, and todorokite MnO2 (Mg0.20MnO2), which contains tunnels of 3x3 octahedra dimensions. When tested as intercalation electrodes in Na-ion batteries, we find that the material with smaller structural tunnels, α-MnO2, achieved a higher initial capacity of 330 mAh g-1, while todorokite MnO2, which contains larger 3x3 octahedra tunnels, achieved a capacity of 157 mAh g-1. However, the larger tunnel structure proved to be more stable in a Na-ion battery, demonstrating superior capacity retention, as well as superior rate performance. These results suggest that although smaller tunnels may initially show higher capacity, larger tunnels are preferable for superior electrochemical stability. Further, the effect of material morphology is also shown by synthesizing todorokite MnO2 with both a platelet and a nanowire morphology. In Li-ion batteries, the nanowire morphology exhibited a 30% higher capacity retention after 100 cycles, demonstrating the advantage of a nanowire morphology in terms of enhanced cycling stability. Moreover, the effect of structural water in todorokite MnO2 (0.42 H2O molecules per Mn) is discussed, elucidating the role of structural water on ion insertion of into tunnel structured materials. Lastly, we discuss the effect of controlling the electrochemical potential window used during cycling, the trade off between capacity and capacity retention, and how the stability of these materials can be improved. This work describes the role of tunnel size, ionic content, and material morphology on the behavior of tunnel manganese oxides and thus provides insight into tailoring of tunnel structured materials for intercalation batteries.