Climate energy balance models (EBMs) – simple energy-balance-based models of climate change – are widely used. The simplest “linear” EBM is deficient in capturing the behavior of complex climate models, so a “two-layer” model with an additional degree of complexity, i.e. two vertical layers, is typically used. Other additional degrees of complexity are equally plausible as well, however, and different approaches to add a degree complexity have not been compared quantitatively. Here we compare four types of EBMs - two-layer, order-two (temperature-dependent feedback), two-region (in space), and two-timescale (fast and slow climate responses) - specifically, their ability to capture historical temperature change and simulated temperature changes in abrupt (4x) and gradual (1%-ramp) forcing scenarios. The two-region model outperforms the others. The two-region model’s best-fit parameters to historical temperatures are also more physically plausible than the next-best-fitting model, the two-layer model. We therefore conclude that the two-region model is the preferred climate EBM.