well, how long is a piece of string?
First of all, there is the signal chain -it was probably recorded in a professional studio using top end mics and pre-amps and who knows what else before voice ever reached tape. Then it would have been shaped by a professional engineer probably using tasteful amounts of EQ and compression..
Agree, nothing to touch Barbara's voice but on listening to the song, apart from what I've just mentioned, the only thing I can detect behind her voice is some light reverb to get that slightly 'distant' sound..
What I'd suggest is record your version, but have Barbara's version on a separate reference track - muted while you are recording of course. Then once done, you can isolate your backing track and compare your voice and vocal tone to the reference. You would then work out if you need any boosts or cuts in the lower, lower mids, mids, upper mids or top frequency range. An EQ will help you with that. Then look at your performance overall - are there softer or louder bits that stand out? Compression will help with that. Have a look on YouTube for tips on vocal compression and EQ.
Oh and best of luck!