We analyze the potential efficiency of laser beam projection onto a remote object in atmosphere with incoherent and coherent phase-locked conformal-beam director systems composed of an adaptive array of fiber collimators. Adaptive optics compensation of turbulence-induced phase aberrations in these systems is performed at each fiber collimator. Our analysis is based on a derived expression for the atmospheric-averaged value of the mean square residual phase error as well as direct numerical simulations. Operation of both conformal-beam projection systems is compared for various adaptive system configurations characterized by the number of fiber collimators, the adaptive compensation resolution, and atmospheric turbulence conditions.