As a prototypical dispersion-dominated physisorption problem, we analyze here the performance of dispersionless and dispersion-accounting methodologies on the helium interaction with cluster models of the TiO2(110) surface. A special focus has been given to the dispersionless density functional dlDF and the dlDF+D-as construction for the total interaction energy (K. Pernal, R. Podeswa, K. Patkowski, and K. Szalewicz, Phys. Rev. Lett. 2009, 109, 263201), where D-as is in effective interatomic pairwise functional form for the dispersion. Likewise, the performance of symmetry-adapted perturbation theory (SAPT) method is evaluated, where the interacting monomers are described by density functional theory (DFT) with the dlDF, PBE, and PBEO functionals. Our benchmarks include CCSD(T)-F12b calculations and comparative analysis on the nuclear bound states supported by the He cluster potentials. Moreover, intra- and intermonomer correlation contributions to the physisorption interaction are analyzed through the method of increments (H. Stoll, J. Chem. Phys. 1992, 97, 8449) at the CCSD(T) level of theory. This conjunction with a partitioning of the Hartree-Fock interaction energy to estimate individual interaction energy components, comparing them with those obtained using the different SAPT(DFT) approaches. The cluster size evolution of dispersionless and dispersion-accounting energy components is then discussed, revealing the reduced role of the dispersionless interaction and intramonomer correlation when the extended nature of the surface is better accounted for. On the contrary, both post-Hartree Fock and SAPT(DFT) results clearly demonstrate the high-transferability character of the effective pairwise dispersion interaction whatever the cluster model is. Our contribution also illustrates how the method of increments can be used as a valuable tool not only to achieve the accuracy of CCSD(T) calculations using large cluster models but also to evaluate the performance of SAPT(DFT) methods for the physically well-defined contributions to the total interaction energy. Overall, our work indicates the excellent performance of a dlDF+D-as approach in which the parameters are optimized using the smallest cluster model of the target surface to treat van der Waals adsorbate-surface interactions.