So has anyone tested if forging at say sky forge actually produces better results than the normal forge near the entrance of white run?

There was no difference in the base damage, at least in the forging menu. Whether they're superior in some other way, I'm not sure.

From what I've noticed, the Skyforge does not have a noticeable impact on the crafted item. If anything, the Skyforge is actually worse as it lacks a tanning rack, smelter, and workbench.

but you can make the 'Nord Hero' armor at the Skyforge