In my experience it's the white bread that has mold grow faster on it than the wheat bread.
Although most commercial made bread contains preservatives to prevent mold growth from happening too soon the white bread must have less preservatives than the wheat bread because white bread in my house always tends to grow mold faster than wheat bread if I don't eat the white bread soon enough.
I keep my white bread and wheat bread in breadbox but still if I forget about it the white bread grows mold faster than the wheat bread does even when both are in the breadbox.