Context. Broad sets of spectroscopic observations comprising multiple lines represent an excellent opportunity for diagnostics of the properties of the prominence plasma and the dynamics of their fine structures. However, they also bring significant challenges when they are compared with synthetic spectra provided by radiative transfer modeling. Aims. In this work, we provide a statistical spectroscopic analysis of a unique dataset of coordinated prominence observations in the Lyman lines (Lyα to Lyδ) and the Mg II k and h lines. The observed data were obtained by the Solar Ultraviolet Measurements of Emitted Radiation (SUMER) spectrograph on board of the Solar and Heliospheric Observatory (SoHO) satellite and the Interface Region Imaging Spectrograph (IRIS) on 22 October 2013. Only a few similar coordinated datasets of Lyman and Mg II k and h observations have ever been obtained in prominences and we present here the first analysis using these two sets of spectral lines. Moreover, for the first time, we assess the influence of noise on the statistical properties of the studied profile characteristics. Methods. We focus on the following profile characteristics: the shape of the observed line profiles based on the number of distinct peaks, the integrated line intensity, the center-to-peak ratio describing the depth of the reversal of two-peaked profiles, and the asymmetry of these peaks. Results. We show that the presence of noise has a negligible effect on the integrated intensity of all observed lines, but it significantly affects the classification of spectral profiles using the number of distinct peaks, the reversal depth, and also the peak asymmetry. We also demonstrate that by taking the influence of noise into account, we can assess which profile characteristics in which spectral lines are suitable for diagnostics of different properties of the observed prominence. For example, we show that the subordinate peaks (peaks below error bars) in the Lyman line profiles are mostly caused by noise, which means that only the dominant peaks should be used for statistical analyses or comparisons with synthetic spectra. On the other hand, in the Mg II k and h profiles, the key role in the distinction between the multi-peaked profiles with low peaks and the profiles with deep reversals is played by the dynamics of multiple fine structures located along a line of sight. The complex, multi-peaked profiles are observed in places where multiple fine structures with different line-of-sight velocities are crossing the line of sight, while the profiles with deep reversals likely correspond to instances when we observe single fine structures or more fine structures but with similar line-of-sight velocities. Conclusions. This study allows us to conclude that if we are interested in the diagnostics of the dynamics of prominence fine structures, the best approach is to use a combination of profile asymmetry in the Lyman lines together with the complex profiles of Mg II k and h lines. On the other hand, if we want to diagnose the temperature and pressure properties of individual prominence fine structures, we need to focus on the deeply reversed Mg II k and h lines in combination with the Lyman lines and to analyze the depth of the central reversal and the integrated intensities.