Parametric models are simpler in form and more straightforward to conduct inference on, as the parameters are fixed no matter the size of the data. However, if a parametric model is assumed for a process, but the data actually was generated from a different mechanism, the model is incorrectly specified, and inference is likely to be suspect.
Non-parametric models provide the flexibility to adapt the parameter space to the data at hand and scale with more data, as they are not reliant on initial assumptions like parametric models are. However, they are more computationally expensive and often less interpretable than parametric models. Also, being non-parametric models are more complex, they are also more susceptible to overfitting.
