We are interested in the following two R^d-valued stochastic differential equations (SDEs): (Formula Presented), where σ is an invertible d × d matrix, L_t is a rotationally symmetric α-stable Lévy process, and B_t is a d-dimensional standard Brownian motion (note that B_t is a rotationally symmetric α-stable Lévy process with α = 2). We show that for any α₀ ∈(1,2) the Wasserstein-1 distance W₁ satisfies for α ∈[α₀,2) [Formula Presented.] which implies, in particular, [Formula Presented.] where μ_α and μ₂ are the ergodic measures of X_t and Y_t respectively. For the special case of a d-dimensional Ornstein–Uhlenbeck system, we show that W₁(μ_α,μ₂)≥C_d (2 − α) for all α ∈(1,2); this indicates that the convergence rate with respect to α in the previous bound is optimal. The term d log(1 + d) appearing in the bound seems to also be optimal for the dimension d.