Metamaterials have emerged as promising solutions for noise control applications as they can achieve superior noise insulation performance in compact designs. While these materials effectively alter objective noise levels, their impact on perceived sound quality remains less understood. This study presents a comparative analysis between efficient analytical transfer matrix models and high-fidelity numerical finite element approaches for predicting the psychoacoustic performance of vibro-acoustic metamaterial partitions and enclosures. An auralization framework is developed to render sound transmitted through metamaterial configurations using filter-based methods. To this end, frequency dependent sound transmission filters based on analytical models and on numerical finite element simulations are used and compared. These are combined with both standardized acoustic stimuli as well as application-representative to generate auralized signals, from which psychoacoustic metrics, including loudness, sharpness, roughness, tonality, and prominence ratio, are extracted and compared against psychoacoustic Just Noticeable Differences. To capture the effects of finite dimensions and boundary conditions of real-world scenarios, the impact of different finite element model counterparts is assessed and compared with analytical infinite structure-based filtering. Specifically, the representativeness of both filters for band-limited and tonal excitations, typically of interest for metamaterial treatment, is distinguished. The European Commission is gratefully acknowledged for its support of the Marie Sklodowska Curie program through the Horizon Europe DN METAVISION project (GA 101072415). Views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union. The European Union cannot be held responsible for them. The research of L. Van Belle (fellowship no. 1254325N) is funded by a grant from the Research Foundation – Flanders (FWO).