Decision trees vs. Neural Networks

I'm implementing a machine learning structure to try and predict fraud on financial systems like banks, etc... This means that there is a lot of different data that can be used to train the model eg. I'm having trouble deciding which structure is the best for this problem. I have some experience with decision trees but currently I have started to question if a neural network would be better for this kind of problem. Also if any other method would be best please feel free to enlighten me.