Speaking as both a singer and a songwriter, I am firmly on the side of #1 on this. Music and songwriting are creative pursuits; I much prefer creativity to a paint-by-numbers approach, so I prefer the people who take what they know of a song as a starting point, and then make it their own. And I REALLY enjoy hearing someone excercising their creativity on one of my own songs, taking it to places that hadn't occurred to me, and incorporating their own thoughts and personality into the song in the process. The songs just have more "life" that way.
Of course, as in all things, some people do this well, and some people do it badly. I prefer to listen to the ones who do it well.