Modern theoretical models of astrophysical jets combine accretion, rotation, and magnetic fields to launch and collimate supersonic flows from a central source. Near the source, magnetic field strengths must be large enough to collimate the jet requiring that the Poynting flux exceeds the kinetic energy flux. The extent to which the Poynting flux dominates kinetic energy flux at large distances from the engine distinguishes two classes of models. In magneto-centrifugal launch models, magnetic fields dominate only at scales less than about 100 engine radii, after which the jets become hydrodynamically dominated (HD). By contrast, in Poynting flux dominated (PFD) magnetic tower models, the field dominates even out to much larger scales. To compare the large distance propagation differences of these two paradigms, we perform three-dimensional ideal magnetohydrodynamic adaptive mesh refinement simulations of both HD and PFD stellar jets formed via the same energy flux. We also compare how thermal energy losses and rotation of the jet base affects the stability in these jets. For the conditions described, we show that PFD and HD exhibit observationally distinguishable features: PFD jets are lighter, slower, and less stable than HD jets. Unlike HD jets, PFD jets develop current-driven instabilities that are exacerbated as cooling and rotation increase, resulting in jets that are clumpier than those in the HD limit. Our PFD jet simulations also resemble the magnetic towers that have been recently created in laboratory astrophysical jet experiments.