We report a complete analysis of model silica/styrene-butadiene rubber (SBR) nanocomposites including a direct and quantitative correlation between the filler structure and the mechanical reinforcement. We compared two different ways of sample processing: a solvent casting route with well-defined colloidal silica and the manufacturing process of internal mixing with industrial silica powder. The multiscale filler dispersion was characterized with a combination of SAXS/TEM in both reciprocal and direct space. The mechanical properties were determined with oscillatory shear measurements. We evaluated the influence of two polymer-filler interfacial additives on the filler dispersion: a coating agent and a coupling agent for different particle concentrations. Using simple analytical functions, we succeed in modeling the filler dispersion. We obtained surprisingly the same general trend whatever the sample processing, solvent casting, or internal mixing. The primary particles form fractal primary aggregates inside the matrix as a result of a diffusion-limited aggregation process driven by the interfacial additive. The coupling agent, which can form covalent bonds with the matrix chains, leads to smaller and denser primary aggregates while the coating one gives rise to larger and more ramified objects. This can be explained by the restriction of nanoparticle diffusion due to covalent bonds. The primary aggregates arrange into a secondary large scale structure, agglomerates, or by a branched network. The spatial correlations between the primary aggregates follow a Percus-Yevick function allowing us to distinguish between more or less interpenetrated networks in a situation of percolation. The viscoelastic behavior of the composites has been analyzed quantitatively with a percolation model. Below the percolation threshold, the reinforcement is mostly driven by the cluster compactness. We highlight a mechanical percolation whose threshold is dependent on the interfacial additive, but not on the material fabrication process, arising at lower filler volume fraction than the structural percolation. Above the percolation threshold, the network modulus varies as the power three of filler network density which is determined from geometrical assumptions. The filler network density, traducing the degree of interpenetration of the aggregates inside the network, is driven by both the interfacial additive and the samples preparation: the coupling agent as well as the internal mixing process gives rise to a denser network with a resulting improved modulus.