Aims. We aim to better constrain the atmospheric properties of the directly imaged exoplanet 51 Eri b using a retrieval approach with data of higher signal-to-noise ratio (S/N) than previously reported. In this context, we also compare the results from an atmospheric retrieval to using a self-consistent model to fit atmospheric parameters. Methods. We applied the radiative transfer code petitRADTRANS to our near-infrared SPHERE observations of 51 Eri b in order to retrieve its atmospheric parameters. Additionally, we attempted to reproduce previous results with the retrieval approach and compared the results to self-consistent models using the best-fit parameters from the retrieval as priors. Results. We present a higher S/N YH spectrum of the planet and revised K1K2 photometry (M-K1 = 15.11 +/- 0.04 mag, M-K2 = 17.11 +/- 0.38 mag). The best-fit parameters obtained using an atmospheric retrieval differ from previous results using self-consistent models. In general, we find that our solutions tend towards cloud-free atmospheres (e.g. log tau(clouds) = 5.20 +/- 1.44). For our `nominal' model with new data, we find a lower metallicity ([Fe/H] = 0.26 +/- 0.30 dex) and C/O ratio (0.38 +/- 0.09), and a slightly higher effective temperature (T-eff = 807 +/- 45 K) than previous studies. The surface gravity (log g = 4.05 +/- 0.37) is in agreement with the reported values in the literature within uncertainties. We estimate the mass of the planet to be between 2 and 4 MJup. When comparing with self-consistent models, we encounter a known correlation between the presence of clouds and the shape of the P-T profiles. Conclusions. Our findings support the idea that results from atmospheric retrievals should not be discussed in isolation, but rather along with self-consistent temperature structures obtained using the best-fit parameters of the retrieval. This, along with observations at longer wavelengths, might help to better characterise the atmospheres and determine their degree of cloudiness.