An experimental investigation of the effect of inlet flow conditions and improved geometries on the performance of modern axial exhaust diffusers of gas turbines has been completed. As the first of a two-part series, this article concentrates on characterizing diffuser sensitivity to parametric variations in internal geometry and inlet flow conditions. Full-factorial experiments were carried out on five parameters including the inlet Mach distribution, shape of the support struts, shape of the oil-drain strut, diffuser hade angle, and the hubcap configuration. To enable an efficient sweep of the design space, experiments were performed in this initial study at a down-scaled turbine exit Reynolds number (Re_H roughly 3% of the value for an H-class diffuser) and at a full-scale turbine exit Mach number. The study was accomplished in a continuous, cold-flow wind tunnel circuit, and tailored distributions of Mach number, swirl velocity, and radial velocity derived from on-design conditions of an industry diffuser were generated. Measurements included 5-hole probe traverses at planes of interest. Diffuser performance was most sensitive to the inlet Mach distribution with losses of 0.081 points of pressure recovery due to a non-uniform Mach distribution with higher velocity near the hub versus a uniform one. Detailed comparisons of axial flow variation for a top-performing configuration versus related configurations shed physical insight regarding the evolution of kinetic energy distortion into viscous loss in the wake, as well as highlight the benefit of uniform inlet profiles in practice despite the lower theoretical recovery of such cases. The results presented here isolate the inlet flow distribution as a parameter of high interest for further study which is carried out for both on- and off-design conditions in the companion article soon to be published.