This work presents the analysis of performance and robustness properties of different INDI architectures, together with the evaluation of the effectiveness of an L1 Piecewise Constant (PwC) adaptive augmentation, designed to compensate for perturbations in the dynamics. Using as application scenario the nonlinear longitudinal dynamics of a tail-controlled airframe, an INDI pitch rate control loop is designed within the cascade of a climb angle autopilot. The differences between model-based and sensor-based INDI control laws are highlighted both in the time-domain and in the frequency-domain, and a sensitivity study is performed with respect to the tuning parameters of the adaptive augmentation. The results highlight performance and robustness tradeoffs in the design of the adaptive controller when considering different baseline INDI architectures, offering valuable insights on the tuning of these innovative control systems.