Massive hydraulic fracturing requires an enormous consumption of water and introduces many potential environmental issues. In addition, water-based fluid tends to be trapped in formations, reducing oil/gas-phase relative permeability, and causes clay-mineral swelling, which lowers absolute permeability. Carbon dioxide (CO2) is seen as a promising alternative working fluid that poses no formation-damage risk, and it can stimulate more-complex and extensive fracture networks. However, very little, if any, extant research has quantitatively analyzed the effectiveness of CO2 fracturing, except for some qualitative fracturing experiments that are based on acoustic emissions. In this study, we systematically examine water and CO2 fracturing, and compare their performance on the basis of a rigorously coupled geomechanics and a fluid-heat-flow model. Parameters investigated include fluid viscosity, compressibility, in-situ stress, and rock permeability, illustrating how they affect breakdown pressure (BP) and leakoff, as well as fracturing effectiveness. It is found that (1) CO2 has the potential to lower BP, benefiting the propagation of fractures; (2) water fracturing tends to create wider and longer tensile fractures compared with CO2 fracturing, thereby facilitating proppant transport and placement; (3) CO2 fracturing could dramatically enhance the complexity of artificial fracture networks even under high-stress-anisotropy conditions; (4) thickened CO2 tends to generate simpler fracture networks than does supercritical CO2 (SC-CO2), but still more-complex fracture networks than fresh water; and (5) the alternative fracturing scheme (i.e., SC-CO2 fracturing followed by thickened-CO2 fracturing) can readily create complex fracture networks and carry proppant to keep hydraulic fractures open. This study reveals that, for intact reservoirs, water-based fracturing can achieve better fracturing performance than CO2 fracturing; however, for naturally fractured reservoirs, CO2 fracturing can constitute an effective way to stimulate tight/shale oil/gas reservoirs, thereby improving oil/gas production.