A previously synthesized hyperbranched poly(butylene adipate) (HPBA) polymer was compared with a commercial dendritic polyol (HPOH) as a toughening agent for a commercial one-part epoxy resin. Both modifiers were added in weight percentages of 1, 3, 5, and 10%. The modified epoxies were characterized using differential scanning calorimetry (DSC), dynamic mechanical analysis (DMA), thermogravimetric analysis (TGA), melt rheological tests, and linear elastic fracture mechanics. Blend morphology and matrix–modifier interactions were evaluated using scanning electron microscopy (SEM) and Fourier transform infrared spectroscopy (FTIR) analysis, respectively. The toughness-improvement effect was achieved without substantial impairment of thermomechanical properties or degradation of the thermal stability of the epoxy resin. A meaningful decrease in viscosity was achieved with both modifiers, contributing to an easier infusion processability. No evidence of new chemical linking was found although phase separation was observed by SEM, leading to the conclusion that only interfacial linkage occurs between modifiers and epoxy chains. SEM analysis also clearly shows the fracture mode changing from brittle to ductile by addition of modifiers, which was more evident for blends of HPBA.