Really hard to quantify what improvements are as they are as subjective as a users preference in sound. In regards to my own pair of HD598, the bass went from sounding too cuppy/boomy, cold, and analytical, to sounding warm, robust, and lush. There was a small change in the midrange as well; on high registers of certain female vocals there was a little bit of glare and strain. After burn-in the vocals smoothed out and gained a little warmth. I saw virtually no change in the treble. Maybe a little more air but I contribute that more to my upgraded cable than burn-in.
In my opinion, either the pack-in cable sounds like poop, or the 6.3mm - 3.5mm adaptor is playing a factor. To me it is VERY noticeable to the point where I would be using the supplied cable to watch a movie (it is long enough to reach while I am on the couch) and when finished decide to listen to music. I would often forget (ok every damn time) I am using the supplied cable and always I think that my music does not sound right. I would then proceed to open up all of the preferences in the OS and music player looking to see if some setting has been changed (like resampling settings or an EQ left on) only to realize after frustration that I am not using the upgraded cable; Upon switching everything sounded right. It's as if the supplied cable adds a rather noticeable veil. Anyway ditch the supplied cable.