I love the covers, you know I do, I love to compare versions of songs. For me, the proof of a great song is that different people can sing it in different ways and still get to the good place; the proof of a good band/singer is that he can take a song that has been done to death by another band/singer and do it justice, or better.
(For an example of the former, check out "Billy Jean" by Caetano Veloso; of the later, check out "If I Needed Someone" by the Hollies.)
Sometimes a song just gets so, so limitlessly, fabulously, wonderfully done to death by some singer that another singer could be forgiven for just giving up the field, uh uh, not going there, that song has been just taken over, that song has become the wholly owned subsidiary of somebody else, somebody that's not me, but it's not necessary really. Songs aren't like that.
The below videos, two singers performing their own, very different versions of "Imagination," display, for me, the whole dynamic of sharing standard songs. Here's the rule: If you love the song, and you can bring the necessary sincerity and respect to it, go ahead on with your bad self, sing the motherfucker. It's okay, don't worry about comparisons, the song loves you and it appreciates the attention.