The goal of this work is to evaluate the efficiency of multi-fidelity (MF), using simple or Bayesian discrepancy approaches, to reduce the required number of high-fidelity simulations in nonlinear constrained optimization problems relevant to aircraft wing design. Our focus is on quantifying the performance of MF methods depending on the number of design parameters describing the wing shape. The rationale is that the inclusion of an MF method in an iterative optimization process requires proof of its effectiveness and the dimension of the design space is an important factor affecting the performance of surrogate models. The efficiency is measured here in terms of the probability that the number of Reynolds-averaged Navier-Stokes flow simulations (the high-fidelity model), which is necessary to solve a design optimization problem, is reduced when using MF compared to the single-fidelity model.