Nirvana version of "where did you sleep last night"

Placebo's version of Running up that Hill is the definitive version. Fight me.

Boys of Summer - The Ataris

Don Henley's 1984 version is nice, but this early 00s power pop version hits so good.

Not really sure if it is relevant to what you're asking, but I think it's so cool. https://youtu.be/NLnfFUZNkww?

Hurt by Johnny Cash

Honestly, most anything by Me First and the Gimme Gimmes, a pop punk band I used to listen to a lot in the oughts that strictly performs covers. Favs include “My Boyfriends Back” “Stand By Your Man” and “Sloop John B”

Hurt - Johnny Cash

I wanna be like you (jungle book) by psychedelic porn crumpets. Give it a try, it's good.

Sultans of Swing (metal cover by Leo Moracchioli feat. Mary Spender)

Cover - check
Popular song - check
From 80s or 90s - check
Redone into metal - check
Female vocalist - check!

Bonus song: Manhattan Skyline by Ihsahn feat. Einar Solberg
It's not harder than the original, but Ihsahn and Einar are some of the most influential metal musicians out there

Johnny Cash's version of Hurt https://open.spotify.com/track/28cnXtME493VX9NOw9cIUh

AWOL nations got a cover album a couple years ago. There is at least one Abba song on it.

Chris Cornell did a couple of covers I cant get enough of. Acoustic Nothing Compares to you.

And a cover/mashup of Metallica's Ones lyrics to U2s One Lyrics which is amazing.

I follow a guy called Leo Morachioli who does metal covers of popular songs. I really enjoy Leo's version of toss a coin to your witcher and also his cover over final countdown. His videos are rad.

Lourdes all along the watchtower is good

Alien Ant Farm did a fun cover of Smooth Criminal is good too

Children of Bodom cover of Oops I Did it Again

Tweeter and the Monkey Man - The Headstones

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

Joe Jacksons cover of Fleetwood Mac's "Oh, Well" rocks! The Ramones cover of the old 1960's Spiderman TV theme song was excellent! Nancy Griffith's cover of "Tecumseh Valley" by Townes Van Zandt always leaves a lump in my throat.

The band Tragedy started out as a heavy metal BeeGees cover band, I believe, but expanded to do hard rock covers of disco, pop, and adult contemporary staples. I'm not a big Abba fan but I love every one of this band's covers and their cover of Madonna's Borderline.

https://music.youtube.com/channel/UCe33AhFCT2agDzBideLHGRw

Thunderstruck by Walk Off the Earth. Female vocalist, a wild twist on instuments that just seems to work. https://www.youtube.com/watch?v=9RnGkIxhFGU

I never found a metal rendition of a 'softer' song that's better than the original so I got nothing on that.

But here's few of some artis I follow.

Eleanor Rigby - Josh Turner I think most of the song he cover is old (idk I don't really listen to classic song). But good lord, he's talented af.

Jack Conte (CEO of Patreon) are on both of these. Pomplamoose is his band with his wife Nataly Dawn.

Scary pockets brings different singer (and other instrument) each song, mostly funk forward.

Pomplamoose - Mr Blue Sky

Just the 2 of us - Scary Pockets

If you like those two, you probably also like Lawrence

This is just straight up jazz but they're super good. Young Original - Its a lovely day today

I like Denzel Curry's cover of Bulls on Parade.

Wind Rose - Diggy Diggy Hole

https://youtu.be/34CZjsEI1yU

I love Shinedown's cover of Simple Man.

I know it's probably not what you're asking for but there's an album where a bunch of Japanese anime voice actresses did covers for popular songs from the 80s and 90s. It called Voice Actresses Legendary Punk Songs Collection and here's a playlist that has most of the songs (one of them is unavailable for some reason).

Outside of that, I mostly only know bands who have covers of video game music (and some movies) from the 80s and 90s. If you are counting those, here are some examples of them:

Lighting Strikes Again and Metal Squad from Thunder Force IV by SSH. SSH is known for metal covers of old video game music, so this is just one example of his music.

Cranial Syphon by Armcannon, which is a cover of some song from Metroid but I'm not familiar with that game so I don't know what it is exactly. On top of covers for other video game music, they also have stuff like the Ghostbuster's theme.

Kraid by Metroid Metal, which is obviously another metroid song (possibly the same one). There music was a bit hard to find on YouTube, I've forgotten where I first heard their music before but Youtube might not be the best platform to find the rest of their music.

Battle Scene from Final fantasy by The Black Mages. While they are currently disbanded, they were known for rock/metal covers of music from the Final Fantasy games (which makes sense given that the band was created by Nobuo Uematsu himself). They did briefly rebrand as "Earthbound Papas" for one album because not only did they want to cover more than just the Final Fantasy games but they also wanted to branch out to more genres.

I know for sure that there are some that I'm forgetting and there's also some that I don't feel like looking for examples for (mainly artists who've covered the music from the 90s era Touhou games). If asked, I may do through and provide them but I think I've provided more than enough already.

In This Moment covered In the Air Tonight by Phil Collins. It's a slow burn, but it's great!

Motörhead - Heroes

Original by David Bowie 1977.

motörhead recorded the cover version while recording their last album in 2015.

Generally I would say I like the music of Bowie better than motörhead, but in this case, their cover of his song is better than the original.

Covers of popular songs

Okay...

from the 80s or 90s

...ah, fuck. Yeah, the original is from 2013 😄

redone today into a hard rock or metal version.

Check!

Bonus if it's a female vocalist.

Well, 2 out of 3 is good enough: Take Me to Church by The Agonist

The standouts for me are A Perfect Circle doing covers of People are People by Depeche Mode and Peace, Love, and Understanding by Brinsley Schwarz.

The Shrek 2 'fairy godmother' cover of I Need a Hero is far more enjoyable than the original one imo.

Others that come to mind have already been listed here..

https://www.youtube.com/watch?v=aC8fsX-B0BE

Love this one: House of the Rising Sun - Lauren O'Connell

https://www.youtube.com/watch?v=Bu_NEFpri0g

GWAR did a cover of Pink Pony Club

It's infinitely better to the original. I known it's a new song. I don't care.