The model-free and model-fitting kinetic approaches have been applied to data for nonisothermal and isothermal thermal decompositions of HMX and ammonium dinitramide. The popular model-fitting approach gives excellent fits for both isothermal and nonisothermal data but yields highly uncertain values of the Arrhenius parameters when applied to nonisothermal data. These values cannot be meaningfully compared with the values derived from isothermal measurements, nor they can be used to reasonably predict the isothermal kinetics. On the other hand, the model-free approach represented by the isoconversional method yields similar dependencies of the activation energy on the extent of conversion for isothermal and nonisothermal experiments. The dependence derived from nonisothermal data permits reliable predictions of the isothermal kinetics. The use of the model-free approach is recommended as a trustworthy way of obtaining reliable and consistent kinetic information from both nonisothermal and isothermal data.