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The dynamics of dense finite-size particles in vertical channel flows of Newtonian and viscoelastic carrier fluids are examined using particle resolved simulations. Comparison to neutrally buoyant particles in the same configuration highlights the effect of settling. The particle volume fraction is $5\%$, and a gravity field acts counter to the flow direction. Despite a modest density ratio ($ρ_r = 1.15$), qualitative changes arise due to the relative velocity between the particle and fluid phases. While dense particles are homogeneously distributed in the core of the channel, the mean concentration profile peaks in the near-wall region due to a competition between shear- and rotation-induced lift forces. These forces act in the cross-stream directions, and are analyzed by evaluating conditional averages along individual particle trajectories. The correlation between the angular and translational velocities of the particles highlights the significance of the Magnus lift force in both the spanwise and wall-normal directions. The collective behaviour of the particles is also intriguing. Using a \Voro analysis, strong clustering is identified in dense particles near the wall, which is shown to alter their streamwise velocities. This clustering is attributed to the preferential transport of aggregated particles towards the wall. The practical implication of the non-uniformity of particle distribution is a significant increase in drag. When the carrier fluid is viscoelastic, the particle migration is enhanced which leads to larger stresses, thus negating the capacity of viscoelasticity to reduce turbulent drag.