We investigate, using theory and simulations, the role of the short and long grafted chains in polydisperse polymer grafted nanoparticles in stabilizing particle dispersion in a chemically similar polymer matrix in the presence of particle-particle attractions. The effect of the short and long chains in a polydisperse or bidisperse graft length distribution on the potential of mean force between the polymer grafted nanoparticles is coupled and distinct from their role in the corresponding deconstructed short and long monodisperse distributions. At high grafting density, the increased monomer crowding near the particle surface from both short and long chains maximizes shielding of particle-particle attraction, while the length and crowding of long chains away from the particle surface determine the location, range, and strength of the steric repulsion and midrange attraction. We find that to maximize grafted nanoparticle dispersion, it is best to synthesize grafted particles at high grafting density with polymer graft length distributions that maximize monomer crowding near the particle surface to shield particle-particle attraction and minimize crowding at farther distances from the particle to increase wetting of the grafted layer by matrix chains. Polydisperse (log-normal) graft length distributions and bidisperse graft length distributions with few long chains among many short chains satisfy this criterion and better disperse grafted particles in a chemically identical matrix than monodisperse grafts or bidisperse graft length distributions with equal number of short and long chains, with equivalent average graft length.