There is an urge to give an answer that it is the same, because they contain the exact same ingredient.
But actually, the answer is strongly dependent on the “fermentable” fiber content of both. There is a very direct correlation of fiber content and sugar metabolism because of IGN-1 expression. Now according to a research paper there is a high amount of resistant starch due to baking processes :
Baking for prolonged period was shown to increase resistant starch content of wheat bread and rye bread (Rabe and Seivert 1992).
Similar effects with a rise in resistant starch content are observed by dehulling legumes by steam treatment and cooking (Tovar and Melito 1996). On the other hand, methods like canning, extrusion and microwave heating have been reported to lower the levels of resistant starch (Periago and others 1996; Meance and others 1999; Marconi and others 2000)
Which is correlated by this study
[Code] [food] [name] [food detail] [highest RS] [Lowest RS] [RS/100g]
1211 Grains (other than rice) e.g. millet, barley, raw oats Barley 16.1 1.6 0.81
1221 Bread, rolls, white 0.91 0.55 0.87
1222 Bread, rolls, mixed grain 0.9 0.9 0.97
1223 Bread, rolls, wholemeal 1.5 0.52 0.87
1224 Bread, rolls, rye, black, pumpernickel Rye 4.5 3.2 1.35
1225 Breads, rolls, white, fibre increased 2.7 0.9 1.77
1226 Breads, rolls, major flour not stated 1.7 1.7 1.17
1232 Breakfast cereal, bran, processed 1.1 0.6 1.22
1233 Breakfast cereal, low sugar, puffed, flakes, extruded single cereal 3.1 2.3 1.53
1234 Breakfast cereal, wheat based biscuits 2.3 1.6 1.12
1235 Breakfast cereal, wheat, low added sugar, puffed, flakes 6.2 1 0.85
1241 English style muffins 1 1 1.01
1242 Crumpets 1 1 0.99
1243 flat breads: lavish, naan, chapati, pitta Lebanese bread 1.6 1.6 0.40
The short answer is that wholewheat bread seems to contain a higher content of resistant starch fiber because of the cooking process, resulting in it being better.