Could you provide more details regarding this question? Both RBF and MLP are universal functions approximators. Therefore, both are able to approximate any function. I think this comparison must be in terms of accuracy or other metric (e.g., MSE, F-measure).

In terms of accuracy Dr. Jordão

In many applications such as signal processing and computer vison MLP provides better results than RBF. In particular, recurrent networks and convolutional neural networks, which are a variation of MLP, are the current state-of-the-art in such applications. However, the computational cost is extremely higher than RBF.

You can do a deeper and robust comparison between RBFs and MLPs by looking for papers from International Joint Conference on Neural Networks (IJCNN) conference. This conference includes papers of both RBF and MLP.

Thank you Dr. Jordão

In fact, I tried RBF for function approximation and the accuracy (the error), even at the training point was not as low as MLP network, specially I think MLP is a better approximator than RBF for high dimension function approximation problems.

RBF networks are sensitive to the initial values of the parameters. The center positions primarily, followed by the widths (sigmas). K-means clustering is a reasonable way to initialize the centers. The sigmas then may be initialized by considering one point to the left (or right) of the center and determine sigma by fitting a Gaussian

Thank you very much Dr. Isaac Lagaris

Of course it depends to the problem; but in most cases RBF has better performance. If you are searching a good classifier, you may be try the SVM. as I studied before in different works, SVM has both good speed in solving the classification problems and good performance for different works

According to my experience, trend of data is an important factor that effects on selection.

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