What is the measurable difference between dry basil and fresh?
In addition to the great answer by M.K: Most industrially dried and fresh herbs are not even of the same exact kind. 

Taking basil as an example: Most basil species don't preserve their aroma well during the drying process. So while you can use any kind of basil for fresh use, you can maybe only use certain kinds for drying, because they preserve the aroma a little bit better. This will of course lead to a different flavor profile, because they are different kinds of basil. 

You can basically divide herbs kind of into "hard" and "soft". "Hard" herbs would be something like rosemary and thyme, which are quite dry and hard, even when fresh. They preserve very well during the drying process and can be used almost identical fresh and dried. "Soft" herbs, on the other hand, wilt easily and many of them become almost tasteless during the drying process. This includes basil, chives, certain kinds of oregano, and to a certain extend parsley. For these herbs freezing is a better preserving method!

Fun fact: there are plants that only get fragrant when dried. Woodruff is a common example of that (although, no one would call that a herb as far as i know). It starts giving of its distinct flavor only when wilting.