Just had time to dip into this thread, but I have read (at leangth) both approaches and my thoughts on them are..
AP - Not convinced by Dr Sears. The evidence he uses to back up his theory is very selective and does not accurately represent the evidence that is out there (he leaves out the bits that does not support his theory). I can honestly say that that is true because after reading his book on AP, I looked up the actual research for myself, and found there to be a number of discrepancies.
My second concern is that AP parents seem to believe in some kind of myth that there is such a thing as non western parenting, and that it is better. They seem to suggest that all non western parents use slings, cosleep and do extended breastfeeding. This is at best naive, but in truth is completely at utterly wrong. Lets take a few examples, the Ik tribes force all their children to leave home at the grand old age of three, and they are left to defend for themselves. Another tribe (forget the name, but I think they are sub saharan Africa) allow the mothers to raise their children until one, when breastfeeding stops, the mother goes out to work the fields etc and the father stays at home to raise the kids. Another Amazonian tribe, does carry children in slings, but they don't actually talk to their children until they are about 2 or three. Therefore, in their society, you can see two year olds who are a pro with a machete, but who cannot talk (Seen a video of this myself, very odd from a western viewpoint!). The point is there is no such thing as 'traditional' parenting that the west has lost sight off, that is a myth and I don't think it is helpful for APers to be purporting such a myth that is so very difficult for parents to have as their golden standard that they feel as though they have got to live up to in western society.
On the other hand, I totally reject GF as I feel as though it does not respect the baby as a person, and I do not agree at all with controlled crying. If I was hungry at 3pm, I'd get some food. If a baby is hungry then, why must they starve just because some book says they should? Just don't get that myself.
Whilst the BW is not perfect (and there are some things that I really disagree with), like the other posters, I feel that it works from a premise of respect for the child, but also that it advocates a routine based around the needs of a child to give structure and order without clock watching. To me, that is a good compromise. I used it with both my children, and both slept through from 8 weeks (using the book) and I never had to use controlled crying with either of them.