I never heard this version until recently and I like it a million times better without the strings. 

Another one:

 

 

That band-only version is on the 25th Anniversary Release of that album.  It also has the string-only version, which is cool in the opposite way.

 

I'll have to look for them on Youtube, but here's three songs that come to mind that have slightly different versions:

 

"Bad Religion" by Godsmack: the original album pressing had an intro of some televangelist, going "The word of God is PRAISE from God. [something something something]. Our righteousness is of Him, sayeth the Lord."  Later pressings of the same album had this removed.  Somehow I got one of these early pressings when I bought it back in high school.  I don't even think many people know this pressing exists, because people seem to think there was only one version of the song (when I looked into it in the 2000s).

"Legs" by ZZ Top: the original album version has a synthesizer, but starts right into the song.  The music video version, which is also the version on some Greatest Hits album, has a fade-in of the synthesizers.

"Rock the Casbah": there's the digitized version and undigitized version of that one line, "That crazy casbah jive".  One version is "...that crazy casbah jiiiive", with no digital manipulation.  The version I like is the one with a digital alteration, where it goes "...that crazy casbah ji-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-i-ive".

 

 

The funk/fast version of Drive by REM.

 

Probably nsfw language

 

 

Just clarifying.... I'm not talking about cover songs. 

I'm talking about alternate takes/remixes/re-recordings/unplugged/different live versions performed by the same band. 

Example:

 

Re-Recording of St. Anger with deeper guitar sound and they fixed the drumming.