As Moore's law slows down, GPUs must pivot towards multi-module designs to continue scaling performance at historical rates. Prior work on multi-module GPUs has focused on performance, while largely ignoring the issue of energy efficiency. In this work, we propose a new metric for GPU efficiency called EDP Scaling Efficiency that quantifies the effects of both strong performance scaling and overall energy efficiency in these designs. To enable this analysis, we develop a novel top-down GPU energy estimation framework that is accurate within 10% of a recent GPU design. Being decoupled from granular GPU microarchitectural details, the framework is appropriate for energy efficiency studies in future GPUs. Using this model in conjunction with performance simulation, we show that the dominating factor influencing the energy efficiency of GPUs over the next decade is GPUmodule (GPM) idle time. Furthermore, neither inter-module interconnect energy, nor GPM microarchitectural design is expected to play a key role in this regard. We demonstrate that multi-module GPUs are on a trajectory to become 2× less energy efficient than current monolithic designs; a significant issue for data centers which are already energy constrained. Finally, we show that architects must be willing to spend more (not less) energy to enable higher bandwidth inter-GPM connections, because counter-intuitively, this additional energy expenditure can reduce total GPU energy consumption by as much as 45%, providing a path to energy efficient strong scaling in the future.