Sorry I disagree (just my opinion of course) but the Sinatra version is haunting, soulful, and passionate. Cher...isn’t any of those things.
No need to apologize for having a different opinion.
After a 2nd listen, I actually don’t like Nancy’s version at all.
Here’s a version by the lunatic Lady Gaga:
https://www.youtube.com/watch?v=uRr4Ma6opuk
Here’s another vid of Cher’s version with her actually singing in it, or pretending to sing. The audio is old and scratchy. In any case, she was pretty cute back in those days.
Cher-Bang Bang (My Baby Shot Me Down) 1966 Music Video
https://www.youtube.com/watch?v=tyfWSa3So7U