Have you ever seen a cover of a band you love just to have the cover beating the original?

Good ole' times with Snoop & The Doors

https://www.youtube.com/watch?v=0VAF-4Er7_A

Radiohead's cover of The Smiths - Headmaster Ritual

https://www.youtube.com/watch?v=LtmS2ePSSdU

Leo plays Adele, and Adele can be forgotten.
https://www.youtube.com/watch?v=LtQUJMBH8uE

Steven Wilson - The Day Before You Came

Zombie from The Cranberries has been covered by many, it's hard to choose. One very underrated is by Breed77:
https://youtu.be/XJFmh6W1Jjo

Aretha Frankiln's "Respect" is way better than the original song, even Redding has admited it :P

A lot of songs by Peter Hollens.

Hopefully I didn't mess the formatting up on that.

I Fought The Law - Clash (Bobby Fuller Four)
Killing Me Softly - The Fugees (Roberta Flack)

Hurt by Johnny Cash is also awesome, but it can't replace the original by Nine Inch Nails.

A lot of the covers I like better often are from a genre I prefer more than the original, so mine are a little biased. A few have already been mentioned, such as Disturbed s covers of other songs, but I also really enjoyed Seethers cover of Careless Whisper.
Also a few pop goes punk like A Day to Remembers cover of Since U Been Gone and Framing Hanley of Lollipop. Not really sure if it beats the original, but it gets close, Johnny Cash covers Hurt That sort of sadness of an old man really hits this song well, something Johnny Cash did well for this cover For me Five Finger Death Punch absolutely killed Bad Companyin a good way. Two covers of Tainted Love, one being Soft Cell and the next Marilyn Manson. There's probably a bunch of other better ones than I have posted below I'm really bad at remembering things on the spot so I'll be sure to update if anybody is interested. ^_^

Careless Whisper
Since U Been Gone
Lollipop
Hurt
Bad Company
Knockin on Heavens Door
Soft CellTainted
MMTainted

Take Five by Tito Puente

Johnny Cash - Hurt

Bastille - No Angels

Maxence Cyrin - Where Is My Mind

Turisas covering Jethro Tull's Broadsword came to mind immediately:

The cover

Original

Anathema - Mountains Made Of Steam (Thee Silver Mt. Zion Memorial Orchestra)

https://youtu.be/32lb8f0QEXE

https://youtu.be/qF9dCWmq3pM

The original is sort of good-ish.
https://youtu.be/ZEvQOPUHGH8