Oscar-winning composer John Barry wrote two demo themes for Once Bitten, but didn't get the job. Undeterred, Barry then recycled the demos into an instrumental called "The Best Man in the World" for the Eddie Murphy vehicle, The Golden Child. If that wasn't humiliating enough, Barry was then replaced on that film after a disastrous test screening.¹
What you are hearing are the demos used in Barry's discarded soundtrack for The Golden Child.² While John Du Prez chose to present a playful, comedy-friendly score for Once Bitten, using a tango for his Main Theme that has a melody reminiscent of the Young Frankenstein love theme, Barry played it straight and went for a stately, moody orchestral score (with a little Body Heat thrown in).
John Barry Prendergast, OBE (3 November 1933 - 30 January 2011) was an English composer and conductor of film music. He composed the soundtracks for 11 of the James Bond films between 1963 and 1987, and also arranged and performed the "James Bond Theme" to the first film in the series, 1962's Dr. No. In a career spanning over 50 years, he received many awards for his work, including five Academy Awards; two for Born Free, and one each for The Lion in Winter (for which he also won a BAFTA Award), Dances with Wolves and Out of Africa (both of which also won him Grammy Awards). In 1999 he was appointed OBE for services to music.
¹ - SOURCES: www.johnbarry.org.uk/filmnotgraphy.php, http://rejectedfilmscores.150m.com/byfilm.html
² - "The Golden Child: Music From The Motion Picture." Score by Michel Colombier / Music Composed by John Barry. La La Land Records - LLLCD 1180 (3 CD Limited Edition of the expanded soundtrack, 2013).