We review twelve invariant and dispersion-type anisotropic hyperelastic constitutive models for soft biological tissues based on their fitting performance to various experimental data. To this end, we used a hybrid multi-objective optimization procedure along with a genetic algorithm to generate the initial guesses followed by a gradient-based search algorithm. The constitutive models are then fit to a set of uniaxial and biaxial tension experiments conducted on tissues with different histology. For the in silico investigation, experiments conducted on human aneurysmatic abdominal aorta, linea alba, and rectus sheath tissues are utilized. Accordingly, the models are ranked with respect to an objective normalized quality of fit metric. Finally, a detailed discussion is carried out on the fitting performance of the models. This work provides a valuable quantitative comparison of various anisotropic hyperelastic models, the findings of which can aid researchers in selecting the most suitable constitutive model for their particular analysis. The investigation reveals superior fitting performance of dispersion-type anisotropic constitutive formulations over invariant formulations.