Neural nets and Genetic algorithm are totally different things which achieve totally different objectives. The neural net is a way to describe a mapping (function) and the genetic algorithm is an optimization process. Thus they cannot be compared.
Neural Networks coupled with Genetic Algorithms can really accelerate the learning process to solve a certain problem.
From an optimization/mathematical point of view, Neural nets are a way to describe a trainable function that is known to perform very well on a wide variety of tasks.
Since NNs required a lot of data, and GAs didn’t. GAs was used mostly to simulate environments and behaviors of entities in a population. They were mostly used to learn the path to a problem that we knew the answer to.
NNs have helped us solve so many problems. But there’s a huge problem that they still have that is hyperparameters(Hyper-parameters are values required by the NN to perform properly, given a problem). These are the only values that can not be learned.
We can use GAs to learn the best hyper-parameters for a NN!
When you create a Tetris bot you do not necessarily have to use an ANN as a function approximator. But you need some kind of function approximator to represent your bot's policy. But when you want to create a complex nonlinear policy you could do that with an ANN.