A decade-long (2010-2020) period with precipitation deficits in central-south Chile (30-41 degrees S), the so-called megadrought (MD), has led to streamflow depletions of larger amplitude than expected from precipitation anomalies, indicating an intensification in drought propagation. We analysed the catchment characteristics and runoff mechanisms modulating such intensification by using the CAMELS-CL dataset and simulations from the HBV hydrological model. We compared annual precipitation-runoff (P-R) relationships before and during the MD across 106 basins with varying snow-/rainfall regimes and identified those catchments where drought propagation was intensified. Our results show that catchments' hydrological memory - modulated by snow and groundwater - is a key control of drought propagation. Snow-dominated catchments (30-35 degrees S) feature larger groundwater contribution to streamflow than pluvial basins, which we relate to the infiltration of snowmelt over the Western Andean Front. This leads to longer memory in these basins, represented by a significative correlation between autumn streamflow (when snow has already melted) and the precipitation from the preceding year. Hence, under persistent drought conditions, snow-dominated catchments accumulate the effects of precipitation deficits and progressively generate less water, compared with their historical behaviour, notably affecting central Chile, a region with limited water supply and which concentrates most of the country's population and water demands. Finally, we addressed a general question: what is worse - an extreme single-year drought or a persistent moderate drought? In snow-dominated basins, where water provision strongly depends on both the current and previous precipitation seasons, an extreme drought induces larger absolute streamflow deficits; however persistent deficits induce a more intensified propagation of the meteorological drought. Hence, the worst scenario would be an extreme meteorological drought following consecutive years of precipitation below average, as occurred in 2019. In pluvial basins of southern Chile (35-41 degrees S), hydrologic memory is still an important factor, but water supply is more strongly dependant on the meteorological conditions of the current year, and therefore an extreme drought would have a higher impact on water supply than a persistent but moderate drought.