Friction dampers can be a cheap and efficient way to reduce the vibration levels of a wide range of mechanical systems. In the present work it is shown that the maximum energy dissipation and corresponding optimum friction force of friction dampers with stiff localized contacts and large relative displacements within the contact, can be determined with sufficient accuracy using a dry (Coulomb) friction model. Both the numerical calculations with more complex friction models and the experimental results in a laboratory test set-up show that these two quantities are relatively robust properties of a system with friction. The numerical calculations are performed with several friction models currently used in the literature. For the stick phase smooth approximations like viscous damping or the arctan function are considered but also the non-smooth switch friction model is used. For the slip phase several models of the Stribeck effect are used. The test set-up for the laboratory experiments consists of a mass sliding on parallel ball-bearings, where additional friction is created by a sledge attached to the mass, which is pre-stressed against a friction plate. The measured energy dissipation is in good agreement with the theoretical results for Coulomb friction.