The early outcome prediction of ongoing or completed processes confers competitive advantage to organizations. The performance of classic machine learning and, more recently, deep learning techniques such as Long Short-Term Memory (LSTM) on this type of classification problem has been thorougly investigated. Recently, much research focused on applying Convolutional Neural Networks (CNN) to time series problems including classification, however not yet to outcome prediction. The purpose of this paper is to close this gap and compare CNNs to LSTMs. Attention is another technique that, in combination with LSTMs, has found application in time series classification and was included in our research. Our findings show that all these neural networks achieve satisfactory to high predictive power provided sufficiently large datasets. CNNs perfom on par with LSTMs; the Attention mechanism adds no value to the latter. Since CNNs run one order of magnitude faster than both types of LSTM, their use is preferable. All models are robust with respect to their hyperparameters and achieve their maximal predictive power early on in the cases, usually after only a few events, making them highly suitable for runtime predictions. We argue that CNNs' speed, early predictive power and robustness should pave the way for their application in process outcome prediction.