What advice would you give an NCO that recently transferred from the Air Force to the Army?

SGT (Join to see) Not a prior Airman, but perhaps helpful advice from someone who has worked with many prior service Soldiers from other branches:
Don't be the guy that mentions they were in the Air Force every 5 minutes or why it is better/worse than your current assignment.

Let your conduct and performance speak for itself. If you want your subordinates to know about your prior service, give them a military bio and encourage them to do one.

This does not mean don't talk about your experiences, we all do it, but do it in a way that is about the lessons learned rather than storytelling mode that might come off in a way that is not intended.

Being a leader in the Army isn't that much different than the expectations in any other branch: Soldiers are entitled to exceptional leadership, you will provide that leadership. Treat all Soldiers with dignity and respect, train them, mentor them, develop them to be better Soldiers and leaders than before they met you.
That means you have work to do in your MOS and in the Army. You have all new systems and programs to learn, utilize and teach.

I didn't serve in separate branches but I did lateral move from Infantry to Data Communications. It was a tough transition but it's doable. The best advice I can have for you is to stay hungry for information and stay humble. Use your knowledge and prior experience but don't get comfortable. You need to supplement what you know with all the little pieces you don't and the only way to fill the gaps is to absorb everything, take notes and learn as fast as you can. Staying humble will help you a lot and prevent building friction with anyone
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Dummy!