Is it better to use separately regularization methods for Neural Networks (L2/L1 & Dropout)
I am unsure there will be a formal way to show which is best in which situations as it depends on many factors like your dataset, architecture of the your ANN  - simply trying out different combinations is likely best.
It is worth noting that Dropout* is actually doing more than just regularization, it makes the model more robust,allowing it to try different nodes for prediction.
As for L1/L2 it just reduces overfitting by penalizing the higher weights.