Designing shaped offset Gregorian reflector systems to operate with several interchangeable feed horns, over frequency bandwidths of more than a decade, with multiple, often conflicting, performance figures of merit such as aperture efficiency, receiving sensitivity, sidelobe levels, and cross polarization isolation is a difficult optimization problem. An additional complication may be that the radiation patterns of all the feeds to be used in the system are not known at the time of the dish designs, as upgrades to the feeds may happen throughout the lifetime of large reflector systems. This paper presents a systematic parametric study to quantify the effects of the main causes of performance degradation in such a system, i.e. reflector diffraction and feed pattern variations. First, ideal Gaussian feed patterns are used in order to isolate the diffraction effects, and then the ideal patterns are varied to model the effect of using wideband feeds exhibiting radiation pattern variations over frequency. It is shown that the peak position in the shaping parameter space of the receiving sensitivity is not strongly influenced by diffraction - although the peak value is, as expected, reduced at lower frequencies. This allows similar feed patterns to be used in different frequency bands to still produce systems operating near the maximum sensitivity. When using non-ideal feed patterns it is shown that, for most performance metrics, diffraction effects dominate the feed variation performance degradation in smaller dishes. This allows possibly relaxed requirements on the radiation patterns of feeds used to illuminate electrically small reflector systems.