These are some factors to consider when choosing a method:
Sample type: The Tauc plot method is suitable for measuring the bandgap energy of transparent materials, while the Kubelka-Munk method is suitable for measuring the bandgap energy of opaque materials.
Absorption coefficient: The Tauc plot method requires a precise measurement of the absorption coefficient, which may be difficult to achieve for weakly absorbing materials.
Scattering effects: The Kubelka-Munk method is less sensitive to scattering effects, which can be a major source of error in the Tauc plot method. However, the Kubelka-Munk method assumes that the material is homogeneous and non-absorbing, which may not be true for some materials.
Measurement range: The Tauc plot method is suitable for measuring the bandgap energy of materials with a narrow absorption edge, while the Kubelka-Munk method can be used to measure the bandgap energy of materials with a broader absorption edge.
Check this for more detailed information: https://doi.org/10.1021/acs.jpclett.8b02892