The effect of plasma shaping on scrape-off layer (SOL) plasma turbulence is investigated through a rigorous validation exercise. Two- and three-dimensional simulations of the SOL plasma dynamics in three TCV limited discharges are carried out with the GBS code. These discharges realize an almost circular magnetic equilibrium, an elongated equilibrium, and an elongated equilibrium with negative triangularity. For the three plasma discharges, three simulations are performed, considering (i) a three-dimensional model with explicit dependence on elongation, triangularity, and inverse aspect ratio; (ii) a circular three-dimensional model in the infinite aspect ratio limit; and (iii) a two-dimensional model which assumes cold ions, infinite aspect ratio, and k//=0. Ten validation observables common to simulations and experimental measurements from a reciprocating probe located at the TCV outer mid-plane are identified and the agreement between experiment and numerical results relative to each observable is evaluated. The composite metric introduced by P. Ricci at al. in [Phys. Plasmas 18, 032109 (2011)] is then used to assess the overall agreement between simulations and experimental measurements. It is found that the shaping model implemented in GBS improves the description of SOL plasma turbulence taking into account the impact of elongation and triangularity and that, in general, three-dimensional simulations are in better agreement with experimental measurements than the numerical results obtained with the two-dimensional model.