I'm not sure that this Ave Maria by Sumi Jo can be considered as a cover but I like it very much. Amazing performance
https://www.youtube.com/watch?v=fjZ8fBGtMaI
I do like covers and sometimes more than the original singer or band. But almost all of the examples I would provide would be of folk music of Brazil's Southern Region so it would make no sense to many and hard to explain the reasons but summarizing the reasons would be that some old folk music here are too much slow and were played with a "slow energy" or something like that. And the same songs in some cover band presentations just by playing a bit faster or singing with more energy made them all more interesting. I could relate it to some songs that in the original were slower than live performance, like this check it out and observe the speed difference:
Breaking the law - Judas Priest, original: https://youtu.be/1cILBcpv2fw
Breaking the law - Judas Priest, LIVE https://youtu.be/L397TWLwrUU
The Trooper - Iron Maiden, original: https://youtu.be/g6NGyE7-jTI
The Trooper - Iron Maiden, LIVE: https://youtu.be/X4bgXH3sJ2Q
I like covers that add something new to the song they cover and aren't just the same song played by another band/musician. When a cover is good, it's usually difficult for me to choose between the original and the cover, because they're both great songs in their own right.
Some of my favourites:
Mad World by Gary Jules (originally by Tears for Fears)
Tainted Love by Marilyn Manson (originally by Gloria Jones)
Hallelujah by Jeff Buckley (originally by Leonard Cohen)
Such Great Heights by Iron & Wine (originally by The Postal Service)