Despite the surge of great earthquakes along subduction zones over the last decade and advances in observations and analysis techniques, it remains unclear whether earthquake complexity is primarily controlled by persistent fault properties or by dynamics of the failure process. We introduce the radiated energy enhancement factor (REEF), given by the ratio of an event's directly measured radiated energy to the calculated minimum radiated energy for a source with the same seismic moment and duration, to quantify the rupture complexity. The REEF measurements for 119 large [moment magnitude (Mw) 7.0 to 9.2] megathrust earthquakes distributed globally show marked systematic regional patterns, suggesting that the rupture complexity is strongly influenced by persistent geological factors. We characterize this as the existence of smooth and rough rupture patches with varying interpatch separation, along with failure dynamics producing triggering interactions that augment the regional influences on large events. We present an improved asperity scenario incorporating both effects and categorize global subduction zones and great earthquakes based on their REEF values and slip patterns. Giant earthquakes rupturing over several hundred kilometers can occur in regions with low-REEF patches and small interpatch spacing, such as for the 1960 Chile, 1964 Alaska, and 2011 Tohoku earthquakes, or in regions with high-REEF patches and large interpatch spacing as in the case for the 2004 Sumatra and 1906 Ecuador-Colombia earthquakes. Thus, combining seismic magnitude Mw and REEF, we provide a quantitative framework to better represent the span of rupture characteristics of great earthquakes and to understand global seismicity.