Systematic uncertainties in the characterisation of helium-dominated metal-polluted white dwarf atmospheres

White dwarf photospheric parameters are usually obtained by means of spectroscopic or photometric analysis. These results are not always consistent with each other, with the published values often including just the statistical uncertainties. The differences are more dramatic for white dwarfs with helium-dominated photospheres, so to obtain realistic uncertainties we have analysed a sample of 13 of these white dwarfs, applying both techniques to up to three different spectroscopic and photometric data sets for each star. We found mean standard deviations of $\left< \sigma {T_{\rm{eff}}}\right> = 524$ K, $\left< \sigma {\log g}\right> = 0.27$ dex and $\left< \sigma {\log (\rm{H/He})}\right> = 0.31$ dex for the effective temperature, surface gravity and relative hydrogen abundance, respectively, when modelling diverse spectroscopic data. The photometric fits provided mean standard deviations up to $\left< \sigma {T_{\rm{eff}}}\right> = 1210$ K and $\left< \sigma {\log g}\right> = 0.13$ dex. We suggest these values to be adopted as realistic lower limits to the published uncertainties in parameters derived from spectroscopic and photometric fits for white dwarfs with similar characteristics. In addition, we investigate the effect of fitting the observational data adopting three different photospheric chemical compositions. In general, pure helium model spectra result in larger Teff compared to those derived from models with traces of hydrogen. The log g shows opposite trends: smaller spectroscopic values and larger photometric ones when compared to models with hydrogen. The addition of metals to the models also affects the derived atmospheric parameters, but a clear trend is not found.