Simpop2 is a generic multi-agent model designed for simulating any system of cities. From an evolutionary theory built upon the observation of networks of cities in different parts of the world and over long time periods, it has been possible to identify stylized facts that characterize their main features and properties. This paper presents data oriented simulations of two kinds of systems: in early settled countries (Europe, 1300-2000) and in countries more recently settled (United States 1650-2000). The model can simulate properly the general dynamics of urban systems, at different scales of observation (general configuration and trajectories of individual cities). The simulations help to identify some dynamic properties that are shared by both systems :1) a general growth trend and spatial expansion (produced through interurban competition which generates emulation towards innovation; this explains the persistency of the hierarchical configuration); 2) a dramatic increase of contrasts in city sizes since the first industrial revolution linked to the increase of communication speed; 3) a differentiation of urban economic functions produced through interactions between cities and innovation cycles, as industrial revolution. The model also put forward the necessary integration of a new urban function in the model, which represents the early emergence of global cities. Yet beyond these similarities in the evolution of all urban systems, when they are fully integrated, the model also measures to what extent the observed peculiarities in their contemporary spatial and functional configuration depend on differences in the early space filling process between the two kinds of systems.