It depends on the function that you are trying to approximate. I can give you a function that a shallow nnet would approximate better and functions that deep n

It depends on the function that you are trying to approximate. I can give you a function that a shallow nnet would approximate better and functions that deep nets approximate exponentially better even with one more layer (in terms of number of neurons n). In the limit n->\infty, both reach arbitrary small errors (obviously often with different number of parameters).