I would try SVM first because the training problem is convex in its parameters. When that doesn't work to satisfaction, ANNs could still be considered. There is no fail-safe way however to tell which one is best for your problem. In particular, the best option may be affected by many factors including (1) the chosen objective function, (2) data sampling and distribution, and (3) dimensionality of the data (number of variables, number of samples).

ANN is a range of classifiers and every training session will produce different classifiers. SVMs have in-built optimizer. In practice if you want to try hard, explore various ANNs. If you just want a reasonable solution fast use SVM.

There is no single technique outperforms all others over the full range of problems. If you provide more information about the problem, data, features, and classes, then maybe selecting the best one will be possible. But in general I prefer SVM.