The operation of single-, double- and triple-THGEM UV-detectors with reflective CsI photocathodes (CsI-THGEM) in Ne/CH4 and Ne/CF4 mixtures was investigated in view of their potential applications in RICH. The studies were carried out with UV, x-rays and {beta}-electrons and focused on the maximum achievable gain, discharge probability, cathode excitation effects and long-term gain stability. Comparative studies under similar conditions were made in CH4, CF4 and Ne/CF4, with a MWPC coupled to a reflective CsI photocathode (CsI-MWPC). It was found that at counting rates <= 10 Hz/mm^2 the maximum achievable gain of CsI-THGEMs is determined by the Raether limit; at counting rates > 10 Hz/mm^2 it dropped with rate. In all cases investigated the attainable CsI-THGEM gain was significantly higher than that of the CsI-MWPC, under similar conditions. Furthermore, the CsI-THGEM UV-detector suffered fewer cathode-excitation induced effects as compared to CsI-MWPC and had better stability at high counting rates.