Determination of the uranium enrichment is an important safeguards verification task, routinely carried out using non-destructive assay methods. The enrichment-meter method is one of the most widely used passive non-destructive X- and gamma-ray based methods used for such tasks. Among its advantages is the highly constrained physical nature of its underlying formalism, allowing it to be used with high-resolution HPGe detectors, as well as with low-resolution NaI detectors. Due to attractive features and spectroscopic performance, CdZnTe and LaBr3(Ce) detectors raised interest in their application to such tasks as well. However, their spectroscopic performance is different to that of the traditional detectors in many ways. Application of the enrichment-meter method requires determination of the net peak areas corresponding to 235U signature photopeaks. The latter requires an adequate algorithm to select the region-of-interest boundaries, which may be sensitive to asymmetrical photopeaks of CZT detectors. In this paper we conduct a performance assessment of a 500 mm3 CZT detector of a quasi-hemispherical design and a 2 × 2 inch LaBr3(Ce) scintillator with the enrichment-meter method using a set of certified uranium standards with enrichment degrees from 0.31% to 4.46% of 235U atomic abundance. We investigate the impact of different methods used for net peak area determination, statistical quality of acquired spectra and size of region-of-interest boundaries on accuracy and uncertainty. We propose an algorithm for symmetrical/asymmetrical region-of-interest boundaries determination and make recommendations on the best combinations of the region-of-interest size and method used for the net peak area determination for each of the detectors. The underlying routines of the algorithm and analysis procedures are described in detail and results are presented.