CIX is a direct converting hybrid pixel detector designed for medical X-ray imaging applications. Its key feature is the simultaneous counting and integrating of absorbed X-ray quanta, which offers, among other benefits, a large dynamic range as well as the opportunity to calculate the average photon energy of the absorbed spectrum. In this work several different Si, CdTe and CdZnTe sensors are characterized and their suitability as sensor materials for a combined counting and integrating system is assessed. The measurements indicate that temporal stability is an issue for the tested CdTe samples, both on short (ms) and long (s) timescales. Furthermore, the homogeneity of the detector response is addressed and interpreted in terms of lateral polarization. The influence of charge sharing and X-ray fluorescence in the sensor materials will be characterized and their impact on the average photon energy reconstruction will be illustrated through simulations and measurements.