Choosing regularization method in neural networks
There are not any strong, well-documented principles to help you decide between types of regularisation in neural networks. You can even combine regularisation techniques, you don't have to choose just one.

A workable approach can be based on experience, and following literature and other people's results to see what gave good results in different problem domains. Bearing this in mind, dropout has proved very successful for a broad range of problems, and you can probably consider it a good first choice almost regardless of what you are attempting.

Also sometimes just picking a option you are familiar with can help - working with techniques you understand and have experience with may get you better results than trying a whole grab bag of different options where you are not sure what order of magnitude to try for a parameter. A key issue is that the techniques can interplay with other network parameters - for instance, you may want to increase size of layers with dropout depending on the dropout percentage.

Finally, it may not matter hugely which regularisation techniques you are using, just that you understand your problem and model well enough to spot when it is overfitting and could do with more regularisation. Or vice-versa, spot when it is underfitting and that you should scale back the regularisation.