Descent obstruction and Brauer-Manin etale obstruction

Let X be a smooth, projective and geometrically integral variety over a number field. We consider two obstructions to the Hasse principle on X V the Brauer-Manin obstruction applied to etale covers of X and the descent obstruction on X. We prove that the first one is at least as strong as the second. Combining this with a recent example of Poonen shows that the descent obstruction is not sufficient to explain all counterexamples to the Hasse principle.