CSP and PV technologies represent energy sources with large potentials. We present cost-supply curves for both technologies using a consistent methodology for 26 regions, based on geoexplicit information on solar radiation, land cover type and slope, exploring individual potential and interdependencies. For present day, both CSP and PV supply curves start at $0.18/kWh, in North Africa, South America, and Australia. Applying accepted learning rates to official capacity targets, we project prices to drop to $0.11/kWh for both technologies by 2050. In an alternative "fast-learning" scenario, generation costs drop to $0.06-0.07/kWh for CSP, and $0.09/kWh for PV. Competition between them for best areas is explored along with sensitivities of their techno-economic potentials to land use restrictions and land cover type. CSP was found to be more competitive in desert sites with highest direct solar radiation. PV was a clear winner in humid tropical regions, and temperate northern hemisphere. Elsewhere, no clear winner emerged, highlighting the importance of competition in assessments of potentials. Our results show there is ample potential globally for both technologies even accounting for land use restrictions, but stronger support for RD&D and higher investments are needed to make CSP and PV cost-competitive with established power technologies by 2050. (C) 2015 Elsevier Ltd. All rights reserved.