http://www.youtube.com/watch?v=FIPPDFpuvhQ
While us US citizens only heard Branigan's version that peaked at #4 in June 1984, in Europe it was a different story with both versions getting airplay. The UK preferred Branigan's version which hit #5 there, but the German chart for the week of July 9, 1984, had Branigan's version at #1 and RAF's at #2!
Branigan was no doubt attracted to the track because one of the co-writers along with RAF was Giancarlo Bigazzi, who had also written Branigan's breakthrough smash "Gloria." However, "Gloria" was orginally an Italian hit in 1979, so she wasn't competing with the original version of the song when she released her cover in 1982.
For any of you unfamiliar with one of the best songs on the 1980s (or just wanna hear it again), here's Branigan's version in a pretty wicked video directed by William Friedkin of The French Connection and The Exorcist fame:
http://www.youtube.com/watch?v=x6veRtF05oo