I would like to know what are the main differences between SVMs and Neural Networks, and what are the problems for which is more appropriate to use the former and the latter.
Maybe you don't want to deal with papers. "Elements of statistical learning" by Hastie, Tibshirani and Friedmann gives a pretty good overview on both. And also its available online.
the main difference is that you could find optimal hyperplanes with SVMs. On the other hand, ANNs can do multiclass classification straight away. Nevertheless, further information can be found in Machine Learning textbooks from Bishop or Murray; as well as in the original contribution on SVM from Vapnik