Two metallic alloys in the quaternary system Fe–Cr–Mn–Ni were irradiated in situ within a transmission electron microscope (TEM) using Xe+ heavy ions in the temperature range of 293–873 K and in the regime of low- (30 keV) and medium-energies (300 keV) with respective maximum doses of around 40 and 140 dpa. The first alloy is the FeCrMnNi high-entropy alloy (HEA) synthesised with the alloying elements close to equimolar composition. The second alloy is a commercial austenitic stainless steel AISI-348 (70.5Fe-17.5Cr-1.8Mn-9.5Ni wt.%), selected as the “low-entropy” counterpart of the FeCrMnNi HEA. Microstructural characterisation was carried out in the TEM with in situ heavy ion irradiation to investigate the role of entropy on radiation induced segregation and precipitation (RIS and RIP). The results demonstrated that among all the irradiation cases investigated, the FeCrMnNi HEA had its random solid solution matrix phase preserved in 80% of the experiments whilst the austenite matrix of the AISI-348 steel underwent RIP in 80% of the cases. It is therefore demonstrated that small differences between two alloys can lead to different radiation responses, confirming the trend that, by tuning the elemental composition superior radiation resistance can be achieved in metallic alloy systems, but emphasising that some of the constitutive core-effects of HEAs are still in need of further confirmation especially when the application of HEAs in energetic particle irradiation environments is considered.