I think it might be a problem with app thinning, as XCode 7.0.1 fixes some problems with this that sounds similar. At least to me it seems like Apple might be fixing this (in their own, slow way)... Here's what Apple announced:
"...
App slicing is currently unavailable for iOS 9 apps due to an issue affecting iCloud backups created from iOS 9 where some apps from the App Store would only restore to the same model of iOS device.
..."
(see https://developer.apple.com/news/?id=092415a&1443125762)
Anyway, I managed to get round this issue by setting up my 6S as a new phone, then followed some articles on injecting bits from other phone icloud backups on my laptop. was a bit of a pain, but managed to get messages and contacts over, the only two bits not backed up separately to icloud (Please Apple can you add messages to icloud!).