We revise two approaches recently introduced for model parameter identification and traffic state reconstruction using macroscopic traffic flow models and based on real and synthetic loop detector data sets. The first method relies on a Bayesian approach for parameter uncertainty quantification, where a bias term is introduced to account for possible model discrepancies with the observed physical system. The study also compares the ability of first and second order models in reconstructing traffic quantities of interest (flow, speed, density). Alternatively, we explore the performances of a Physics Informed Neural Network (PINN) strategy applied to traffic state estimation and parameter identification for first order models, which gives a good approximation of the underlying dynamics even with poor information consisting in averaged density or flow data at few fixed space locations.