Not necessarily "better" and some will consider a few blasphemy, but I most certainly enjoy these more than the originals:
Ensiferum - Battery (really true to the original actually, but with some tasteful adjustments to give it more balls)
Blind Guardian - Dream a Little Dream of Me (genre preferences play a big role here, and Hansi is just epic)
Sonata Arctica - I Can't Dance (vastly superior vocals)
Axel Rudi Pell - Hallelujah (epic raspy vocals and the children choir is a nice addition. There are many solid covers of this song though)
Iced Earth - Screaming for Vengeance (I prefer the modern sound and like Jon's riffing)
Powerglove - Gotta Catch em' All (Pokemon theme song) (some major nostalgia blended with some awesome power metal)