We study the chemical evolution of the thick and thin discs of the Galaxy by comparing detailed chemical evolution models with recent data from the AMBRE Project. The data suggest that the stars in the thick and thin discs form two distinct sequences with the thick disc stars showing higher [alpha/Fe] ratios. We adopt two different approaches to model the evolution of thick and thin discs. In particular, we adopt: i) a two-infall approach where the thick disc forms fast and before the thin disc and by means of a fast gas accretion episode, whereas the thin disc forms by means of a second accretion episode on a longer timescale; ii) a parallel approach, where the two discs form in parallel but at different rates. By comparing our model results with the observed [Mg/Fe] vs. [Fe/H] and the metallicity distribution functions in the two Galactic components, we conclude that the parallel approach can account for a group of alpha-enhanced metal rich stars present in the data, whereas the two-infall approach cannot explain these stars unless they are the result of stellar migration.