Total integral cross sections-for scattering of oxygen molecules on krypton and xenon atoms were measured in the thermal energy range, as a function of the collision energy and under a controlled alignment of the rotational angular momentum of the molecules [Aquilanti er nl., Nature, 371, 399 (1994)]. Data obtained with a "hot" effusive molecular beam, which contains fast rotating and randomly oriented O-2 molecules, mainly probe the spherical component of the potential energy surfaces. Experiments with supersonic seeded beams, where the oxygen molecules are cooled at the K = 1 rotational level and selectively aligned [Aquilanti et nl., Phys. Rev. Lett. 74, 2929 (1995)], probe the anisotropy of the potential energy surfaces. The analysis of the experimental results, based upon close-coupling exact quantum mechanical calculations of the cross sections, provides an accurate characterization of the interactions at intermediate and large intermolecular distances for the Kr-O-2 and Xe-O-2 systems. It is found that the most stable configuration of the two complexes is for perpendicular approach of the rare gas atom, with energies 15.84 for Kr and 17.87 meV for Xe, at intermolecular distances of 3.72 and 3.87 Angstrom, respectively. An adiabatic approximation and a semiclassical description Shed light on some general features of the collision dynamics of aligned molecules, in particular on the observed effects of the interaction anisotropy on the glory interference phenomenon.