The long-term variability study over a range of black hole mass systems from the microquasars of stellar-mass black holes to the active galactic nuclei (AGNs) of supermassive black holes, in rays offers new insights into the physics of relativistic jets. In this work, we investigate the -ray variability of 11 AGNs–including seven blazars, two unclassified blazar candidates, one radio galaxy, and one narrow-line Seyfert 1 galaxy, along with two microquasars. We employ the damped random walk stochastic process to model approximately 15 years of Fermi-Large Area Telescope (LAT) light curves, revealing rest-frame timescales ranging from 40 to 400 days. The characteristic timescales observed in AGNs are comparable to the optical timescales of accretion disks. Notably, the timescales of jet emission in microquasars closely resemble those of AGNs, indicating consistent jet properties across black holes of all masses. The observed rest-frame timescales in AGNs overlap with both thermal and nonthermal timescales associated with the accretion disk and jet, respectively, suggesting a scaled relationship between and black hole mass (). Although the rest-frame gamma-ray timescales of microquasars deviate significantly from the relation observed in AGNs, they still follow a distinct scaling with in the gamma rays explicitly. These findings offer new insights into the origin of jets and their emission processes. Furthermore, this study suggests an alternative perspective that the properties of relativistic jets or their emission mechanisms may be independent of black hole mass.