Revised Trial: Correct? According to Andre Joost advice, I tried with "+towgs84=0,0,0", and the both two ways seem to get the same answer that mkennedy posted below. So, just to make sure, anybody ...
There is a common formula for computing the initial bearing for a course from lat1, lon1 to lat2, lon2. (And yes, I'm aware that the course will change when traveling). atan2( sin(lon2-lon1) * ...