[chengtao]

As you pointed out the transforming features is powerful, I believe that's the exact reason which makes SVM powerful. Though the way features can be combined with SVM is limited, the limitation makes SVM training fast in the dual space.

On the other hand, if you wanna compare logistic regression with SVM. While the detail is pretty tricky. One simplified view is to compare linear SVM which is essentially hinge loss with L2 regularization against logistic regression with L2 regularization which is essentially negative binomial log likelihood loss with L2 regularization. If you plot the loss functions, it's easy to see how they penalize negative & positive cases differently.