In reply to Northern Mountain Monkey:
No experience claiming on any of these, however...
Last year in Kyrgyzstan we all took out BMC insurance which we found expensive, but it was a condition of receiving a grant from them for the trip.
Another team out there had some members climbing with just the AAC cover. I think they were happy with this but there is a general concern that it comes with quite a small S&R limit I believe. Ultimately I think it doesn't cover you for very many hours (minutes!) of helicopter flight time (for instance). I would have to check the details to confirm.
In the alps, there are other threads on here of people's AAC experience which in easily accessible areas is apparently normally positive.