In this paper, we compare the optical and electrical performance of different Fresnel-based HCPV systems equipped with different refractive secondary optical elements (SOEs) through both optical modelling and experiments. The SOEs (designed with a thorough optical modelling): i) Dielectric-cross compound-parabolic concentrator (DCCPC), ii) (SIngle-Lens-Optical element) SILO-Pyramid, iii) Refractive truncated pyramid (RTP) and, iv) Trumpet; are fabricated (made of PMMA) and mounted on commercially available concentrator solar cell assemblies. An indoor characterisation of all these HCPV units, under controlled conditions, using a CPV Solar Simulator "Helios 3198" is performed. The angular behaviour of the HCPV units is predicted properly, in general, although the measured optical efficiencies result in lower values than in the optical simulations. The reasons for those differences are explored through some fabrication and mounting imperfections detected, among others. The impact of changed irradiance and spectrum is analysed separately. No high dependence in the efficiency or in the acceptance angle, in terms of the maximum power point, was found due to changes in the irradiance. For changed spectral conditions, the decrease in the fill factor results in up to around 4% lower than the maximum values. Moreover, the impact of the spectrum on the acceptance angle was analysed. The results showed an increment of the power-based acceptance angle for blue-rich spectra for the HCPV units with SOEs working as light pipes. From the results of efficiency and acceptance angle, none of the SOEs produces a notably performance than the others.