The difference between believers as "children of God" and as "sons of God" is brought out in Rom. 8:14-21. The Spirit bears witness with their spirit that they are "children of God", and, as such, they are His heirs and joint-heirs with Christ. This stresses the fact of their spiritual birth (verses 16 and 17). On the otherhand, "as many as are led by the Spirit of God, these are sons of God". Their conduct gives evidence of the dignity of their relationship and their likeness to His character.
Matt. 5:9 "blessed are the peacemakers, for they shall be called the sons of God, and verse 44, 45, "Love your enemies and pray for them that persecute you, that ye may become sons of your Father which is an Heaven". The disciples were to do these things not in order that they might become children of God, but that being children they might make the fact manisfest in their character, might "become sons". See 2 Cor. 6:17, 18.
Also, for Scriptures where Jesus by His Holy Spirit and power indwells believers and molds their character in conformity to His likeness, See: Rom. 8:10; Gal. 2:20, 4:19; and Eph. 3:17.