Well… I did search for a while before asking and noticed perhaps my question itself has something basically wrong after reading this and this but still not sure so decided to cry out loud :).

As someone unfamiliar with statistics, recently through this post I was somewhat shocked to learn that R-squared value is not a suitable metric for nonlinear models and began to wonder what's proper for measuring goodness-of-fit of a nonlinear model.

Another blog in the previous link suggests using standard error, but it looks like just a personal view. Is there any consensus for this issue? If not, how to decide what metric should be used? Simply throw the specific model to this site and ask?