Claim: whole grain (specifically wheat) bread is healthier than white bread.
Source: Stack Exchange podcast #55
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Nutrition is a tough area to make strong black-and-white statements.
Bread preference is correlated with other health-affecting lifestyle choices, so we can't just measure the health of people who prefer one bread over another.
It's hard to do a randomised, double-blind, controlled trial over the lifetime of a large sample of people, substituting wholemeal bread for white bread.
It is made worse, because the area has a lot of mixed results and contradictory band-wagons (at least, in the public eye).
Some nutrients are needed (or need to be avoided) by a small proportion of the population, and may be of little consequence to otherwise healthy individuals.
"White bread", "brown bread" (or even "wheat bread") are not tight specifications of bread, but, rather broad categories.
The issue of white versus brown bread was already raging in 1924.
So I cannot give a simple answer.
What I can say is "there is a difference". If the original claim was meant to imply they are nutritionally identical (as opposed to merely equally healthful), it is incorrect.
We studied the rates at which solid and liquid leave the stomach after meals of wholemeal and white bread by using a double isotope technique. There was no difference in the rates at which the solid phases of the gastric contents left the stomach but liquid left the stomach significantly more rapidly with white bread than with wholemeal bread. Furthermore, the amount of liquid leaving the stomach unaccompanied and therefore unbuffered by solid was significantly greater after while bread than wholemeal bread. These findings may be of significance in the pathogenesis of duodenal ulcer and they provide a rational basis for a possible form of dietary treatment.
To deal with this quandary, I am going to look at some individual nutrients. Note: This approach risks the fallacy of composition. It may be that some combination of nutrients has more or less effect that the individual nutrients would suggest. For example, it has been shown that adding bran to wheat bread reduces iron absorption. We therefore need to treat these results with some care.
(I have done this with a number of the most obvious nutrients, until I started to get bored. I avoided cherry-picking; every nutrient I researched is included here. If there are other nutrients worth including, please add a comment or edit it in.)
In alphabetical order:
Eating brown bread over white bread increases the intake of calcium from other sources - specifically milk-products. 66% of pregnant women are calcium deficient.
Wholewheat bread has three times the level of dietary fibre of white bread. Insufficient fibre in North American diets is common and associated with a large number of gastrointestinal disorders.
Further, intake of whole grains have been reliably associated with lower rates of colorectal and gastric cancers, and maybe endometrial cancer and coronary heart disease.
Wheat bread provides more iron that unfortified white bread, and about the same as iron-salt-fortified white bread. (Watch out the for the bran though - see above.) Iron deficiency is a prevalent form of malnutrition world-wide. While less common in North America, it still causes thousands of deaths.
Whole wheat bread has more B-6 in it that white bread, and about the same as B-6 fortified white bread. However, B-6 is slightly less available after eating whole wheat bread.
You absorb more zinc from eating brown bread. A quarter of the world's population is zinc-deficient.
While attempts to answer with a definitive study are missing, by looking at the individual nutrients involved, whole-wheat bread offers more of a number of nutrients associated with better health, with a proviso that bran can reduce iron absorption, and that fortification of white-bread can remedy many of these differences.
Also, white bread tastes better! :-)