The recent encounters with two C-type rubble-pile asteroids, Bennu and Ryugu, confirmed that their internal density was 1.2 gcm−3, lower than the density of the previously explored S-type rubble pile Itokawa, 1.9 gcm−3. As these are the only three rubble piles investigated in detail to date, little is known on how subtle differences in internal density of similarly shaped asteroids could affect surface slopes and thus downslope movement, particularly in near-Earth asteroids whose spin periods are affected by YORP. We modelled surface slopes for a range of internal densities and spin periods for seven small asteroid shape models to understand how differences in internal density of similarly shaped asteroids affect surface slope sensitivity to changes in spin period.We found that for similarly shaped asteroids with spin periods under 6 to 8 h small differences in internal density can affect the slope sensitivity of different asteroids to changes in the spin period. Using the metric of 50% of the surface over 40° slope, as a proxy for catastrophic resurfacing, we found that for 6 of the 7 shape models catastrophic resurfacing would occur at <2.6 h for an internal density of 1.9 gcm−3 compared to <3.2 h for an internal density of 1.2 gcm−3. While this is not a large difference in spin periods, the result that lower density asteroids have surface slopes that are more sensitive to changes in the spin period suggests that low-density rubble piles (e.g. C-type) may have more evidence of downslope motion compared to similar shaped higher density rubble piles (e.g., S-type). The majority of the asteroid shape models investigated were spinning-tops, however, results from the Itokawa shape model hint that irregularly shaped asteroids are more sensitive to spin period changes than top-shaped asteroids, which may help explain why Itokawa has extensive lowlands compared to Ryugu and Bennu’s more rocky surfaces. Our study shows that for similarly shaped asteroids both density and spin periods are critical for determining surface stability and evolution.