Frank,
I didn't go with an AASP because unless you have bought your computer with them you will go to the back of the repair queue which in the two AASPs I tried was 2-3 weeks.
The main goal here is for you to have your PowerBook repaired and returned to you with minimum inconvenience to yourself. Whether that is achieved via an AASP, The Apple Store or Apple (UK) is in effect irrelevant 😉
Allow me to give you an example where an AASP assited me in a way that no one else could:
After approximately 8 months of buying by 12" PowerBook 867MHz the superdrive failed. It could read CDs/DVDs but would not burn. I went to my local AASP to get it repaired under warranty. Once they confirmed that the SuperDrive was faulty they ordered a new one from Apple which took 5 days to arrive. Under normal circumstances my PowerBook would have been with them during those five days however, because of the relationship I had with them, they allowed me to keep the PowerBook and would call me as soon as the replacement superdrive arrived. I got a call 5 days later and took it in at around 3pm. At 10am the following morning I got a call advising me that the work is now complete and I could collect the powerbook. Total inconvenience in time to me = 19hrs (ie overnight). Total cost to me = £0.00 (all done under warranty)
In a previous reply you mentioned MacWarehouse in Brentford as one AASP you approached. They wouldn't have been my first choice because their focus is in box shifting. It's a call centre environment there.
Find an AASP which is a small company in terms of employees. The 2 AASPs that I have a good relationship with have a combined workforce of 12 people in total including directors. Heck, they both have a coffee mug reserved for me. 😉
RD