Johnson-Cook constitutive model is still the most used model in metal cutting simulation, although several drawbacks reported in the literature. A high number of Johnson-Cook model parameters can be found in the literature for the same work material. One question that may arise is "What is the most suitable set of Johnson-Cook model parameters for a given material?". The present paper puts in evidence some issues related with the selection of these parameters from the literature. In this contribution, two sets of Johnson-Cook model parameters for Ti-6A-4V are evaluated, using three types of metal cutting models. These models are based on three different formulations: Lagrangian, Arbitrary Eulerian-Lagrangian (ALE) and Couple Lagrangian-Eulerian (CEL). This evaluation is based on the comparison between measured and predicted chip geometry, chip compression ratio, forces, plastic deformation and temperature distributions.