This depends on the problem and dataset. Several NNs are trained to classify the same set of text documents with SVM and their effectiveness is measured. The performance of the two tools is then statistically compared.
For text classification (TC), the performance of NNs is statistically comparable to that of the SVMs even when a significantly reduced document size is used.
It is found that not only NNs are very viable TC tools with comparable performance to SVMs, but also that it does so using a much-reduced size of the document. The successful use of NNs in classifying reduced text documents would be its great advantage as a classification tool, compared to others, as it can bring great savings in terms of computation time and costs.
Deep Neural networks typically perform better on a large dataset. On smaller application domains, you either have to choose a very small network (in which case SVMs will probably perform better) or you need very good techniques to keep the network from overfitting.