This study aimed at elucidating the contribution of chemical interactions, water binding, and steric hindrance on the effect of wheat and oat brans and of their fractions, i.e., soluble and insoluble, on dough and bread properties. For such purpose, an inert filler, i.e., glass beads of comparable particle size and with no water binding capacity and moisture sorption properties, was also studied. The glass beads provided breads most similar to the control, indicating the limited role of steric hindrance. Brans and bran fractions showed distinct compositional and physical properties. The soluble fraction from oat bran, rich in β-glucan, was less hygroscopic than the wheat counterpart and could bind more water, resulting in larger detrimental effects on bread quality. The β-glucan content showed a prevalent role in affecting gluten development, the thermo-setting behaviour of the dough, and crumb texture, i.e., cohesiveness and resilience. Overall, the comparison between the two brans and their fractions indicated that the interplay between water binding, mainly provided by the insoluble fraction, and the plasticizing properties of the soluble bran fraction controlled the effects on bread volume and texture. From a compositional standpoint, β-glucan content was a determining factor that discriminated the effects of wheat and oat brans.