Recurrent neural networks (RNNs) have long been an architecture of interest for computational models of human sentence processing. The more recently introduced Transformer architecture has been shown to outperform recurrent neural networks on many natural language processing tasks but little is known about their ability to model human language processing. It has long been thought that human sentence reading involves something akin to recurrence and so RNNs may still have an advantage over the Transformer as a cognitive model. In this paper we train both Transformer and RNN based language models and compare their performance as a model of human sentence processing. We use the trained language models to compute surprisal values for the stimuli used in several reading experiments and use mixed linear modelling to measure how well the surprisal explains measures of human reading effort. Our analysis shows that the Transformers outperform the RNNs as cognitive models in explaining self-paced reading times and N400 strength but not gaze durations from an eye-tracking experiment.