For me, covers are always at a disadvantage. Memories create a strong bias, so it is difficult for me to prefer a cover...
With that said, I found TWO covers that, for me, are as good as or better than the original recordings. Interestingly, both are by the same artist and on the same album:
a. River (Joni Mitchel) covered by Sarah McLachan (Wintersong)
b. Happy Christmas (War is Over) by John Lennon, again covered by Sarah McLachan (again on Wintersong.
Happy Listening...