No particular kind of movement wins. Balance work, martial arts, tai chi, swimming, all of it helps about as much, and what predicts the benefit is moving regularly at all.

What the research says

Randomised trials of resistance training, which looks nothing like cardio, produced a moderate reduction in depressive symptoms, and the reduction did not depend on whether strength actually improved. That is a fairly direct sign that quite different forms of movement can arrive at the same place. Those trials were in depression rather than attention, so read across with some care.

Strength of evidence: one line of research. A single study, or a theoretical account.