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When we look up the two expressions largely in the English text, we find:
Sons of God Gen. 6:2; Gen. 6:4; Job 1:6; Job 2:1; Job 38:7; Matt. 5:9; Lk. 20:36; Rom. 8:14; Rom. 8:19; Gal. 3:26
Children of God Jn. 1:12; Jn. 11:52; Rom. 8:16; Rom. 8:21; Rom. 9:8; Phil. 2:15; 1 Jn. 3:1; 1 Jn. 3:2; 1 Jn. 3:10; 1 Jn. 5:2
It is interesting that the expression, “sons of God,” especially in the Old Testament, has a heavenly, more than an earthly feel. That is, “sons of God” are often angels. And in Luke 20:36 Jesus speaks of those who are resurrected from the dead as “sons of God” who are like angels. The “revelation of the sons of God” in Romans 8:19 also refers to the kingdom of God, which is yet to come, for which we hope and wait. The “sons of God” therefore seem to be the children of God who reign with Him in His kingdom. “Sons of God” therefore seems to focus more on our future hope and role in the kingdom. It seems to me that “sons of God” and “children of God” are used almost interchangeably in Romans 8. I think the point of Romans 8 is not to distinguish some Christians (“sons of God”) from other Christians (“children of God”), but to distinguish all Christians from unbelievers. (This, by the way, is his argument, starting in Romans 6. How can we who have died to sin, continue to live in sin? If we are saved then we are no longer of the world, and we should no longer act like we are of the world. We should act like God’s children, like His sons.) Thus, unbelievers are those who are “in the flesh” (8:6-9, 13), and all believers are “in the Spirit” (8:9, etc.) or “led of the Spirit.” I believe that the Spirit of God is at work in us, even when we are not aware of it, and not just when we actively seek His guidance (though this is surely commanded and desirable).
The fatal flaw, I think, to a distinction between the two expressions comes in Galatians 3:26, which says, “For we are all sons of God through faith in Christ Jesus.” That doesn’t sound like an elite group of faithful saints to me.