Although I'd heard the OST version (when seeing the film) previously, the first recorded version I owned was the re-recording (the Billy Strange arrangement) on the vinyl LP: Nancy's Greatest Hits ... one the reasons I bought the LP (in my early teens) was for that song. This was early 1970s and at that time, here in the UK, the OST for You Only Live Twice was generally unavailable ... a while later I bought a 2nd hand US import copy which had been played by a rusty nail instead of a diamond stylus. Not quite the worst LP I spent my pocket money on but pretty close!
A few years later the JB007 scores were re-released on the Sunset label and I was able to replace that album.
For a while I think I preferred the pop version ... but like most pop it wears thin after a while and I found that the more delicate vocal and arrangement is much more satisfying ... and something I'm happy to hear time and again. I have CD versions of both and I enjoy the pop version (I like a lot of Ms. Sinatra's songs) but there's no contest as to which is the better (more enjoyable) version for me.