Sparse Direction-of-Arrival (DOA) estimators depend on the regularization parameter λ which is often empirically tuned. In this work, conducted under the vectorized covariance matrix model, we are looking for theoretical equivalence between the Maximum Likelihood (ML) and sparse estimators. We show that under mild conditions, λ can be chosen thanks to the distribution of the minimum of the ML criterion in the case of two impinging sources. The corresponding λ choice is θinvariant, only requiring an upper bound on the number of sources. Furthermore, it guarantees the global minimum of the sparse ℓ0-regularized criterion to be the ML solution. Numerical experiments confirm that, for the proposed λ, sparse and ML estimators yield the same statistical performance.