I've heard of controversy over the proper direction, like here in North America where the two methods diverge by a bit.
Some Muslim groups in North America take the rhumb line to Mecca (southeastwards) as theirqibla (praying direction) instead of the traditional rule of the shortest path, which would give a northeastward direction from the Eastern USA[citation needed].
http://en.wikipedia.org/wiki/Rhumb_line