Understanding atmospheric escape in close-in exoplanets is critical to interpreting their evolution. We map out the parameter space over which photoevaporation and core-powered mass-loss dominate atmospheric escape. Generally, the transition between the two regimes is determined by the location of the Bondi radius (i.e. the sonic point of core-powered outflow) relative to the penetration depth of extreme ultra-violet (XUV) photons. Photoevaporation dominates the loss when the XUV penetration depth lies inside the Bondi radius (RXUV < RB) and core-powered mass-loss when XUV radiation is absorbed higher up in the flow (RB < RXUV). The transition between the two regimes occurs at a roughly constant ratio of the planet’s radius to its Bondi radius, with the exact value depending logarithmically on planetary and stellar properties. In general, core-powered mass-loss dominates for lower gravity planets with higher equilibrium temperatures, and photoevaporation dominates for higher gravity planets with lower equilibrium temperatures. However, planets can transition between these two mass-loss regimes during their evolution, and core-powered mass-loss can ‘enhance’ photoevaporation over a significant region of parameter space. Interestingly, a planet that is ultimately stripped by core-powered mass-loss has likely only ever experienced core-powered mass-loss. In contrast, a planet that is ultimately stripped by photoevaporation could have experienced an early phase of core-powered mass-loss. Applying our results to the observed super-Earth population suggests that it contains significant fractions of planets where each mechanism controlled the final removal of the H/He envelope, although photoevaporation appears to be responsible for the final carving of the exoplanet radius valley.