In many polymer nanocomposites, stiffness increases steadily as nanofiller content rises, while tensile strength often reaches a maximum at low loading and then drops with further addition. This mismatch between modulus and strength is commonly linked to dispersion quality and the filler-matrix interface, but it remains difficult to quantify which failure mechanism dominates for a given microstructure. Here, we develop a dispersion-resolved finite element framework to quantify failure-mode contributions using phase-field modeling. A representative volume element (RVE) of a polymer matrix with randomly distributed nanofillers is loaded in uniaxial tension. Matrix cracking is captured by a phase-field formulation, and progressive filler-matrix debonding is represented with an interface damage law so that cracking in the matrix and separation along the interface can emerge and compete naturally. Different dispersion states are generated by controlling nearest-neighbor spacing statistics, and interfacial fracture resistance is varied to represent changes in adhesion. Beyond predicting the macroscopic stress-strain response and strength, the model provides a failure-mode breakdown. The relative contributions of matrix cracking, interfacial debonding, and filler damage are extracted by partitioning the dissipated fracture and interface energies together with associated crack measures. Parametric results show that poor dispersion promotes early interface-driven damage and accelerates strength degradation at higher loadings, even though stiffness continues to rise. Improved dispersion and tougher interfaces delay interfacial failure, shift the strength peak to higher filler contents, and reduce the severity of post-peak degradation. The proposed approach offers a practical way to connect dispersion and interface quality to strength stability, and to calibrate effective interfacial properties from measured strength-content curves.