None is better than the other. It all depends on the nature of dataset you have. It is advisable to try out both on your dataset and select the best performing one.
You need to be more explicit with what you want to do. RSM is widely used for optimization. While ANN is a machine learning statistical approach that can be applied in a wide range of data analysis including optimization. So, you need to know what you want to achieve.
Thanks Daniel, yes as you mentioned I would like to make optimization for some parameters that could effect on the process and I'm guessing there are different results in two analysis just I want to see is my hypothesis is true. Many thanks
They both can be used depending on your material and objective. In my opinion, ANN should be more adequate as it can be improved on based on the nature and size of your data, the number of neurons, and your transfer function. That is to say, you could achieve any level of accuracy with ANN by tweaking so many conditions. However, the same may not be said for RSM. My advise is for you to use both methods in your study, then compare the results and choose one for further study. Below are some published articles comparing RSM and ANN based on different applications.
The aim of RSM is analize of data with least experiment and give you a mathematical relation. But ANN need more data. Therefore if percition is your major aim you must use ANN and if time and low experiment is major aim you can use RSM