We invert a global phase-anomaly database of intermediate- to long-period Rayleigh waves, recently updated with increased coverage in the European-Mediterranean region, on a global scale with a higher resolution parameterization in the region of interest. We first compare phase-velocity inversions based on ray and finite-frequency theory and derive for each a corresponding set of local phase-velocity dispersion curves (one per model pixel) between 35 s to 300 s period. Effects of the two different theories on the three-dimensional upper-mantle structure are investigated by inverting each dispersion curve for radial shear-velocity profiles. The combination of a gradient-descent method and a random-Monte-Carlo model search provides an estimated shear-velocity model with associated uncertainties for depths between 40 km to 400 km. While differences between ray-theoretical and finite-frequency models are small compared to model uncertainty, comparisons with independent models favor the finite-frequency one.