LiveStrong says that bran flakes are nutritionally comparable in health to shredded wheat. However, bran flakes contain sugar, while shredded wheat does not. I don't work in the area of life sciences, and googling for health information yields all manner of rationale of why each of two options is good. Can those with an understanding of diet and physiology provide some pro/con considerations for each option?
The European Union has only accepted two health benefits from the consumption of wheat bran
Increase in faecal bulk The claimed effect is ‘intestinal health: faecal bulking’. The target population is assumed to be the general population. The panel considers that an increase in faecal bulk might be a beneficial physiological effect. In weighing the evidence, the panel took into account that the majority of the human intervention studies showed a consistent effect of wheat bran fibre on faecal bulk and that no threshold dose for the effect can be established. A linear dose dependent relationship was demonstrated in several studies. The claimed effects are ‘gut health’ and ‘intestinal transit time, intestinal health’. The target population is assumed to be the general population. In the context of the clarifications provided by Member States, the panel assumes that the claimed effect refers to a reduction in intestinal transit time. The panel considers that a reduction in intestinal transit time within the normal range might be a beneficial physiological effect. In weighing the evidence, the panel took into account that the studies provided consistently indicated that wheat bran fibre consumed at an amount of at least 10 g/day decreased intestinal transit time.
The claim for nutrients provided by wheat bran would likely have been rejected on account of the anti-nutrient phytic acid which is tightly bound to minerals
Most of the minerals in wheat kernels are present as complexes with phytic acid. Mature wheat grain has high phytase activity, hydrolysing phytates and making the minerals nutritionally available (Brinch-Pedersen et al. 2002). However, the presence of phytate has been considered as an anti-nutrient in humans because of its effect on the bioavailability of iron, magnesium, zinc and calcium. While the mechanism is not entirely understood, it is suggested that phytic acid binds strongly with these mineral cations to form phytate–mineral complexes, changing their solubility, functionality absorption and digestibility (Rickard and Thompson 1997). Consequently, the complex cannot be absorbed or easily hydrolysed by the human body and so there is an adverse effect on bioavailability of minerals (Harland and Harland 1980).
so the status of nutrient access from wheat bran remains unclear.
Those issues don't apply so much to shredded wheat which is the whole grain being cooked and shredded as the amount of phytic acid is much less.