Images of asteroids (162173) Ryugu and (101955) Bennu acquired by the Hayabusa2 and OSIRIS-REx missions, respectively, reveal rocky worlds covered in rubble. These two asteroids do not have hydrostatic shapes, indicating that they possess some internal friction and/or cohesion even if they lack tensile strength. Understanding the deviation of the surfaces of these bodies from those of idealized shapes helps constrain the mechanical properties of their interiors. Here, we focus on the feedback between YORP-induced spin-up (in which asymmetric reflection and re-emission of solar radiation from the surface systematically change the rotation rate), long-wavelength topography (which provides a structure to control the orientation), and surface roughness on Ryugu and Bennu. By performing spherical harmonic analyses of the shapes of these two asteroids, we find that although they are superficially similar, they exhibit different long-wavelength topography that implies different internal structures and rotational histories. Bennu's shape and rotation rate require a modest amount of internal strength through some combination of at least 17° of internal friction or a few Pa of cohesion, whereas Ryugu could be nearly strengthless. Bennu's longitudinal ridges make it susceptible to YORP spin-up, consistent with the observed increase in rotation rate that is not seen on Ryugu. These longitudinal ridges also suggest a heterogeneous density structure for Bennu, consistent with gravity data.