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Power consumption in buildings show non-linear behaviors that linear models cannot capture whereas recurrent neural networks (RNNs) can. This ability makes RNNs attractive alternatives for the model-predictive control (MPC) of buildings. However RNN models lack mathematical regularity which makes their use challenging in optimization problems. This work therefore systematically investigates whether using RNNs for building control provides net gains in an MPC framework. It compares the representation power and control performance of two architectures: a fully non-linear RNN architecture and a linear state-space model with non-linear regressor. The comparison covers five instances of each architecture over two months of simulated operation in identical conditions. The error on the one-hour forecast of temperature is 69% lower with the RNN model than with the linear one. In control the linear state-space model outperforms by 10% on the objective function, shows 2.8 times higher average temperature violations, and needs a third of the computation time the RNN model requires. This work therefore demonstrates that in their current form RNNs do improve accuracy but on balance well-designed linear state-space models with non-linear regressors are best in most cases of MPC.