I'd like to preface this by saying.... This is pure speculation, and conjecture purely for the purpose of spawning debate and or discussion.
Considering the process of deriving one or the other is completely different, I would suggest that DME is far different than LME. I did my currently fermenting stout with all DME. The smell was different. It didn't seem to have that crazy, malty, fill your house with malt goodness thing happening. However... I noticed when I tasted my post top-up sample there was good malt flavor, however, it didn't seem to have the incredible sweetness of the syrup.
Here comes the speculation part.... I would have to guess that the things that get left behind during the slow evaporation process of making LME may be different to things in DME due to the fast spray drying process. There may actually be some chemical difference between the two. Maybe not, but logic (maybe not good logic) would believe me to think this. It is never easy to get the same results with the same materials through two different processes. Also, materials left in a liquid state will probably change more, and more quickly than materials in a powdered state.... thus the freshness being an issue. I.E. Wheat flour in water develops gluten even without being kneaded or mixed, the longer the two are combined the more gluten develops, though not at the rate it would if stirred. So, I would say, other than being derived from the same material, and being fundementally made up of the same elements, DME and LME are drastically different.