This is not about time complexity of the both RSM and ANN, it is about their relevance. Overall, which will you recommend if you have to choose one of them?
Needless to say, ANNs are most popular in any aspect that you care to name such as accuracy, easiness and speed. Generally here are a couple of works which have been done by ANN and Adaptive Neuro-Fuzzy Inference System (ANFIS). They can be really work to model complex and nonlinear system. You ought to try them:
Article Applications of Artificial Neural Networks in Information Sy...
Conference Paper Using a Dynamic Neural Network for Thermal Modeling of the L...
Conference Paper Application of Adaptive Neuro-Fuzzy Inference System for Mod...
Conference Paper A computational intelligence method to estimate capacitance ...
Conference Paper Neuro-fuzzy system identification for remaining useful life ...