You might want to also take a look at maxent classifiers (/log linear models).
They're really popular for NLP problems. Modern implementations, which use quasi-newton methods for optimization rather than the slower iterative scaling algorithms, train more quickly than SVMs. They also seem to be less sensitive to the exact value of the regularization hyperparameter. You should probably only prefer SVMs over maxent, if you'd like to use a kernel to get feature conjunctions for free.
As for SVMs vs. neural networks, using SVMs would probably be better than using ANNs. Like maxent models, training SVMs is a convex optimization problem. This means, given a data set and a particular classifier configuration, SVMs will consistently find the same solution. When training multilayer neural networks, the system can converge to various local minima. So, you'll get better or worse solutions depending on what weights you use to initialize the model. With ANNs, you'll need to perform multiple training runs in order to evaluate how good or bad a given model configuration is.