Directionality of a class of partially coherent cosh-Gaussian beams propagating in atmospheric turbulence is studied. It is shown that two partially coherent cosh-Gaussian beams may generate the same angular spread,and there exist equivalent partially coherent cosh-Gaussian beams which may have the same directionality as a fully coherent Gaussian laser beam in free space and also in atmospheric turbulence. The theoretical results are interpreted physically and illustrated numerically.