While molecular property prediction is well-established, reaction property prediction is in its infancy. To date, it is unclear what kind of information including chemical connectivity, reaction rules or three-dimensionality structure are most relevant to accurately infer reaction properties. We contribute to this domain by introducing EquiReact, an equivariant neural network to infer properties of chemical reactions, built from three-dimensional structures of reactants and products. We allow for the inclusion of chemical reaction rules, in the form of atom-mapping, if available. The competitive performance of the model is illustrated for the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS and Proparg-21-TS datasets, ranging in molecular size and reaction class. We show that, compared to state-of-the-art models for reaction property prediction, EquiReact offers: (i) a flexible model with reduced sensitivity between atom-mapping regimes, (ii) better extrapolation capabilities to unseen chemistries, (iii) impressive prediction errors for datasets exhibiting subtle variations in three-dimensional geometries of reactants/products, (iv) reduced sensitivity to geometry quality and (v) excellent data efficiency. Interpretation of the latent representation shows that EquiReact uses different information (distances and angles) to make accurate barrier predictions compared to more chemically-structured baselines SLATM_d and Chemprop.