We have computed a suite of simulations of propagating three-dimensional relativistic jets involving substantial ranges of initial jet Lorentz factors and ratios of jet density to external medium density. These allow us to categorize the respective active galactic nuclei (AGN) into Fanaroff–Riley (FR) class I (jet dominated) and FR class II (lobe dominated) based upon the stability and morphology of the simulations. We used the Athena code, and more recently, the Athena++ code, to produce a collection of large 3D variations of jets, many of which propagate stably and quickly for over 100 jet radii, but others of which eventually become unstable and fill up slowing advancing lobes. Comparing the times when some jets become unstable to these initial parameters allows us to find a threshold where radio-loud AGNs transition from class II to class I. With our highest resolution, fully 3D relativistic simulations we can represent the jets more accurately and thus improve upon and refine earlier results that were based on both our now high-resolution 3D and 2D simulations.