Ok chaps (& chappesses!), will be interesting to see what crops up on this one.
For me my favourite has to be Elton’s take on Lucy in the Sky with Diamonds. One of the very few Beatles covers (IMO of course) which betters the original.
Shock horror - blasphemer I hear you say! Just a bit of fun and not to be taken seriously!!
There ain’t no such animal. 
Someone taking it seriously already I see! I did say IMO, other opinions are nonetheless permitted 
You do understand the use of the “double negative”?
I am a man of simple brain, especially this time of night 
I live in hope someone will answer the question, otherwise I will look like the fool on the hill - see what I did there?!
Another “wee dram” needed….
Seriously though, I can’t recall ever hearing a version of any of their songs where I’ve thought “yes, that’s better”. Mostly I’ve found that the singer of the cover is “trying too hard to be different”.
However I then have a problem trying to think of any covers that I like more than the original.
Strong tea for me - hopefully I will still get some sleep tonight 
Just to emphasise it doesn’t necessarily have to ‘beat’ the original in your opinion. I was just expressing mine! All contributions welcome!
But it’s good if it is better. 
Dear Prudence by either Siouxsie and the Banshees or Trouble Tribe spring to mind
I like Frampton’s version on his Now album too
Tom Petty, Prince, Jeff Lynn, Steve W and Dhani Harrison covering While My Guitar gently weeps at George H’s tribute show was pretty rad…
There are few covers of Beatles songs I have liked (as opposed to album covers = artwork). I intensely disliked Joe Cocker’s With a little help from my friends, i know there’s been something relatively recently that I quite liked, but can’t think what it was. The best cover I can think of off the cuff is Deep Purple’s rendition of We can work it out, from their Mk 1 line-up’s second album, The Book of Taliesyn.
I’m looking through you - Steve Earle
LINKS
Qobuz: I’m Looking Through You by Steve Earle
Tidal: I’m Looking Through You by Steve Earle
Spotify: I’m Looking Through You by Steve Earle
And Spooky Tooth - I am the Walrus
LINKS
Qobuz: I Am the Walrus by Spooky Tooth
Tidal: I Am the Walrus by Spooky Tooth
Spotify: I Am the Walrus by Spooky Tooth
.sjb
Prince blows them all away - you could see the shock on their faces, they couldn’t keep up
‘I Wanna Be Your Man’ - The Rolling Stones
Sergio Mendes & Brasil 66 The Fool On The Hill
Always liked the Sarah McLachlan version of Blackbird.
Much better version of “My sweet lord”. 
