I don't have anything valid to back up my claims here, so take what i have with a grain of salt unless you find external validation for it. That being said i will venture a guess:

Yes and no. Neural networks have a lot of nice properties like being easier to grasp, easier to parrallelize(?) and have better tools which i guess is because neural networks are applicable to more problems than SVM's because they are extensible.( see https://en.wikipedia.org/wiki/Recurrent_neural_network for example).

Either way SVM's still do what they do very nicely and in the field of "Human Activity Recognition" where i did my thesis neural networks are practically never used but SVM's pop up from time to time.