For engines the engine manual carries more weight than the AMM every time.
Where no conflicting data exists in the AMM, of course you use the engine manual!
My statement was to indicate that the AMM is the overriding authority where data exists in both the AMM and engine manual, which is at odds with your post.
As far as the AMM not being an approved document - In Australia at least, every time work is done on an aircraft it MUST be in accordance with approved Data, if the AMM isn't approved data, then I'm in the Poo!!!
K