I like both. It's nice to hear someone else's version - for instance Tibor's cover of Mike's cover of Cook's Tune. I also enjoy hearing music that has been inspired by fans. I guess what I am saying is that I just like music, covers, inspirations, originals, whatever.
I generally get most excited by good original compositions. That said, it's always great to hear a cover that presents an old work in new clothes. I think trying to closely recreate the original presents interesting challenges to the musician/engineer, and it's impressive to hear when something does get close...but perhaps also a little less inspiring. It's all good, I guess!