The division of amyloid protein fibrils is required for the propagation of the amyloid state and is an important contributor to their stability, pathogenicity, and normal function. Here, we combine kinetic nanoscale imaging experiments with analysis of a mathematical model to resolve and compare the division stability of amyloid fibrils. Our theoretical results show that the division of any type of filament results in self-similar length distributions distinct to each fibril type and the conditions applied. By applying these theoretical results to profile the dynamical stability toward breakage for four different amyloid types, we reveal particular differences in the division properties of disease-related amyloid formed from α-synuclein when compared with non-disease associated model amyloid, the former showing lowered intrinsic stability toward breakage and increased likelihood of shedding smaller particles. Our results enable the comparison of protein filaments' intrinsic dynamic stabilities, which are key to unraveling their toxic and infectious potentials.