Absolute pitch is often an obstacle in ear training. Speaking as someone who got the highest grade in a few college-level ear-training courses in music degree programs, the students with perfect pitch had a lot of problems that I didn't. Transposition in particular gave them problems. A really strong sense of relative pitch is much more valuable, especially for areas like jazz theory.
This is really interesting in that it suggests there may be a tradeoff between being good at two advantageous but somewhat mutually exclusive capabilities. On the one hand "perfect" pitch allows people to recognize sounds precisely, but relative pitchers are better pattern recognizers.
This ties in to my anecdotal observation that a lot of these early and seriously instrument-playing kids seemed really bad at judging general musical aesthetics and improvisation, but at the same time really perfect at straight reproduction. By the same token, musically creative people seemed to experiment a lot, often doing a bunch of really interesting improvisations without giving it much thought.
One of my music teachers was this way, it really was something else listening to him just idly talking and playing around on the piano for entire lesson. On the other hand, he was really bad at identifying individual notes but he could re-play a melody that he heard just once without any problems, immediately going off on several tangents and experimenting on it in different keys.
On a personal note, that was the point where I recognized that I was in neither of these categories. I switched my art class to painting after a while and stayed there ;)
Next to that, performers of early music of non-western music experience no advantage from pp. Tunings are relative to other central tones, or tuning does not happen in tempered system currently in use.
