We investigate these two materials as cathodes for Na-ion batteries and find that upon first discharge, the ordered phase exhibits a capacity nearly 300 mAh g-1, while the disordered phase exhibits a capacity of just below 200 mAh g-1. Upon further cycling, however, the disordered phase maintains a greater amount of its initial capacity, indicating that although the better defined tunnel structure may be advantageous for greater initial ion intercalation capacity, the disordered phase shows a greater degree of electrochemical stability. The rate performance of these two materials is discussed in relationship to the different diffusion pathways present in the materials, as well as the structural stability of the two phases upon repeated ions insertion and deinsertion. The performance of these materials is also compared to tunnel manganese oxides with pure tunnel configurations, and the advantage of having such a hybrid tunnel configuration is also emphasized. This work highlights the performance of two similar novel cathode materials for Na-ion batteries, as well as the relationship between the degree of structural order in manganese oxides and their electrochemical behavior in Na-ion batteries.