Equilibrium climate sensitivity (ECS) and transient climate response (TCR) are both measures of the sensitivity of the climate system to external forcing, in terms of temperature response to CO2 doubling. Here it is shown that, of the two, TCR in current-generation coupled climate models is better correlated with the model projected temperature change from the pre-industrial state, not only on decadal time scales but throughout much of the 21st century. For strong mitigation scenarios the difference persists until the end of the century. Historical forcing on the other hand has a significant degree of predictive power of past temperature evolution in the models, but is not relevant to the magnitude of temperature change in their future projections. Regional analysis shows a superior predictive power of ECS over TCR during the latter half of the 21st century in areas with slow warming, illustrating that although TCR is a better predictor of warming on a global scale, it does not capture delayed regional feedbacks, or pattern effects. The transient warming at CO2 quadrupling (T140) is found to be correlated with global mean temperature anomaly for a longer time than TCR, and it also better describes the pattern of regional temperature anomaly at the end of the century. Over the 20th century, there is a weak correlation between total forcing and ECS, contributing to, but not determining, the model agreement with observed warming. ECS and aerosol forcing in the models are not correlated.