As I understand SD 29 only provides guidance for instructor training and qualification.
CAP 720 (also see 719), and CAP 737 provide advice on CRM.
EU-OPS provide advice in AMC OPS 1.943, but identifying any difference between this and what is actually taught is probably a closely guarded secret.
Cynically, I suspect that FAA operators are similar – you will be told exactly what you require, but it will be exactly as written in FARs.
Caution in comparing civil and military ops. Apart from the obvious differences, CRM depends on culture – in the widest sense. Mil and civil do not necessarily share the same aspects of culture.