In an LDS-BSA Newsletter last year, the Young Men General Presidency addressed these questions:
"The duty of all Aaronic Priesthood holders is to 'invite all to come unto Christ.' The objective of Scouting as given by Lord Baden-Powell is to '...bring about God's Kingdom on earth.'
"The new Duty to God positions the activities provided through Cub Scouts, Boys Scouts, Varsity Scouts and Venturers as even more relevant in the development of these Priesthood Men of God.
"As the Young Men General Presidency, we fully support the four programs of Scouting and strongly encourage you to see them effectively utilized in your ward. These are tools that supplement Duty to God in developing strong, well-rounded, self-reliant priesthood men of God who love the Lord with all their heart and are going about, engaged in His work."
This is made even more clear when combined with the special Priesthood/Scouting training broadcast in 2007. The talk by Dallin H. Oaks was actually a conversation between Elder Oaks, Elder Holland, a Seventy, a Stake President and a Bishop. (Note: I found the segment easier to follow watching the video rather than just reading the transcript, because of the format.)
The main idea was that Young Men leaders should be using Duty to God to focus on Young Men's spiritual growth and Scouting (again, in countries where Scouting is used in the Church) for other areas of personal growth:
Elder Snow: Well, I personally believe that if they'll thoughtfully consider the requirements of Duty to God, what's set forth in the pamphlets, it'll become pretty self-evident what's most important - the spiritual development of our young men. A lot of the other physical activities and physical requirements - citizenship requirements - that will be sorted out by our Scouting program.
Elder Oaks: ...focus on the spiritual strength and priority of the Fulfilling [Your] Duty to God program and the uniquely successful activities program of the Scouts.
When used well, Scouting, Duty to God and Aaronic Priesthood instruction should all fit together seamlessly. The separate programs should all overlap and fit together to help build the young men into what God wants them to become:
David L. Frischknecht: I guess that's a little bit why it's difficult for me when I hear comments like, "Well, on Wednesdays we do Scouts, and on Sunday we have our quorum instruction," and, "When are we supposed to do the Duty to God Award?" Well, everything is purposing to help Aaronic Priesthood holders fulfill their duty. And this weaves into all of the - it must weave into their individual lives - in their quorum lives, including their quorum activities.
We have a good example of how to combine all of these things together in the boat story told by Bradley D. Harris in Trails to Testimony (you can read the story here). He explains that quorum activities - Scout activities - should become a laboratory for what is learned on Sunday.
David Pack has also emphasized how Scouting activities can be combined with and enhance the spiritual instruction that should be taking place: "I love 50 milers and what it does for a boy....Tuesday night at the campfire program, you will never see a more teachable group of boys, never better. Someone needs to be there to teach them. Sunday lessons will never be the same. Each boy has accomplished the hardest thing in his life up to that point, which makes him able to do more."
Elder Oaks finished off the segment with these words:
"Thank you. Brethren, we thank you for your time and attention. You have a sacred trust to teach and help young men learn and fulfill their duty to God; this includes the meaning of covenants and the significance of the promised blessings. We hope you have caught the spirit of what we have tried to teach in this discussion. We've spoken of Fulfilling Our Duty to God as a priesthood program that involves important priesthood duties now and leads to the three M's - Melchizedek Priesthood, mission and marriage in the temple.
"We've stressed that a young man's fulfilling his duty to God is about becoming what God wants him to become. That requires us to concentrate on young men fulfilling requirements listed under 'Priesthood Duties and Standards,' 'Family Activities,' 'Quorum Activities,' and 'Spiritual Development.' The other requirements, which overlap Scouting, are of lesser importance for the purpose of this priesthood program.
"Finally, priesthood leaders and parents need to administer this Fulfilling Our Duty to God program as an opportunity to bless the lives of our young men. As you follow this counsel, the Spirit will inspire you, and you will see this program in a new light.
"I invoke the Lord's blessing upon you in your vital responsibility to help young men fulfill their duty to God and thus put their feet on the pathway to the temple.
"This is the work of the Lord; I testify of it and invoke His blessings upon you."
I would strongly encourage you to watch the entire segment and either read or watch the rest of the broadcast too, if you can find the time. It will strengthen your understanding and testimony of both Scouting and the Duty to God program.
I think for Primary leaders, the same ideas can be applied to Faith in God for Boys and Cub Scouting. They can work together and become one seamless program, if leaders will listen to the Spirit.