We reanalyse the potential of the LHC to discover new Z′ gauge bosons and to discriminate between various theoretical models. Using a fast LHC detector simulation, we have investigated how well the characteristics of Z′ bosons from different models can be measured. For this analysis we have combined the information coming from the cross section measurement, which provides also the Z′ mass and total width, the forward-backward charge asymmetries on- and off-peak, and the Z′ rapidity distribution, which is sensitive to its uū and dd̄ couplings. We confirm that new Z′ bosons can be observed in the process pp→Z′→ℓ+ℓ-, up to masses of about 5 TeV for an integrated luminosity of 100 fb-1. The off- and on-resonance peak forward-backward charge asymmetries AFBℓ show that interesting statistical accuracies can be obtained up to Z′ masses of the order of 2 TeV. We then show how the different experimental observables allow for a diagnosis of the Z′ boson and the distinction between the various considered models.