I found the special edition in my Steam folder free of charge so I decided to fire it up and well.....We have MAJOR lag issues, which I find odd couse my PC (although old) can play the older version of Skyrim flawlessly yet it can barely run the Special Edition. I'll still keep it on my PC but I'll probably stick to the older Skyrim and get the Special Edition for the PS4.

That should not be surprising. The special edition has more demanding system requirements that the original edition.