This paper presents a detailed analysis of sensitivity of various second-order and third-order compensated inductive power transfer (IPT) converters, designed for achieving load-independent current (LIC) or load-independent voltage (LIV) output, against input voltage variation. Comparisons of sensitivity for varying input-side inductances are systematically investigated through theoretical circuit analysis and extensive simulation studies. Relationship between second-order and third-order compensation is also explored through the transformation between voltage sources and current sources. The sensitivity analysis provides a convenient guidance for parameter design of IPT systems for achieving the required LIV and LIC operation under wide input range. Besides, the analysis effectively reveals the roles of extra input-side inductors in making the equivalent current source less sensitive, and hence provides a direct and handy interpretation of the choice of higher-order compensation circuits for applications addressing wide ranges of input variations.