SVMs really do not scale well to big datasets. LinearSVM scales better, but not as well as other models, such as XGBoost.

They really shine at small datasets with many features tough. There just is something to the "infinite dimensionality" of a SVM with RBF kernel that really squeezes all the juices of a small-but-wide dataset.

The other shiny part of SVMs is they are dead simple to tune. You basically have two variables: the RBF kernel parameter and the regularization coefficient. When in a hurry, SVMs work really well as a go to classifier that gives you nice results with little to no effort.