Metals observed in the atmospheres of white dwarfs suggest that many have recently accreted planetary bodies. In some cases, the compositions observed suggest the accretion of material dominantly from the core (or the mantle) of a differentiated planetary body. Collisions between differentiated exoplanetesimals produce such fragments. In this work, we take advantage of the large numbers of white dwarfs where at least one siderophile (core-loving) and one lithophile (rock-loving) species have been detected to assess how commonly exoplanetesimals differentiate. We utilise N-body simulations that track the fate of core and mantle material during the collisional evolution of planetary systems to show that most remnants of differentiated planetesimals retain core fractions similar to their parents, whilst some are extremely core-rich or mantle-rich. Comparison with the white dwarf data for calcium and iron indicates that the data are consistent with a model in which $66-6+4\%$ have accreted the remnants of differentiated planetesimals, whilst $31-5+5\%$ have Ca/Fe abundances altered by the effects of heating (although the former can be as high as $100\%$, if heating is ignored). These conclusions assume pollution by a single body and that collisional evolution retains similar features across diverse planetary systems. These results imply that both collisions and differentiation are key processes in exoplanetary systems. We highlight the need for a larger sample of polluted white dwarfs with precisely determined metal abundances to better understand the process of differentiation in exoplanetary systems.