I have to say that I still feel the same way about a country cover of "Lose Yourself" after listening to it. I've never had great love for country, but then I'm not a huge rap fan either, yet to me that cover/ version is only good for the same reason as the original, lyrically this still works even if I don't believe Kasey whereas I did believe Marshall, that this was (or at least seemed) their only way out, but, nothing new was brought to the table IMHO.
Johnny Cash's "Hurt" is an example where the performance was transformative. Reznor's "Hurt" is a song by a 20-something addict feeling sorry for himself. However Cash is a man who knows he actually doesn't have much time left†, and so almost identical lyrics ("Crown of shit" is changed) feel very different.
† Cash died about a year after his recording was published.