What is your data? What are its properties? What are you interested in finding out from the data?
Neural networks (NN) fall into the category of Supervised Models. That is, your data will be a set of rows, where each row contains an input and a corresponding output for that input. Your NN learns by seeing the difference between the correct output and one it predicted, and then adjusting its parameters. So you can't use NN if you don't have input-ouput data (generally speaking).
Genetic algorithms (GA) are basically optimizers. Here you will have some set of parameters that you want to optimize for something. You will need an evaluation function that takes these parameters and tells you how good these parameters are. So you keep changing these parameters somehow until you get an acceptable value from your evaluation function, or until you see that things are not improving any more.
To wrap up, if you have data that is suitable for supervising a model, then you can use a NN. If you want to optimize some parameters, then use a GA. But most importantly, it is the nature of your data and what you want out of it that should decide what model to use.