There's a reason that Chris Cornell was at the forefront of the grunge movement. 

Cornell had it all. He could not only sing like an angel, but you could feel the pain, anger, and hurt in his voice when he wanted you to. He was also great with an instrument in his hands as well. 

When you hear a song, you're hearing every guitar, vocal, bass, drum, and more track, all mixed into one. When you isolate one track, you might get a different feeling about the song. Sometimes it's good, sometimes it's bad. 

In the case of isolating Chris Cornell's vocal tracks from "Black Hole Sun," it's definitely a good thing. It's a sliver of proof that he was one of the best in rock. 

(Pardon the strange picture on the video) 

And for fun, here's a screecher [Vocals start at 1:27]: