The "all authority" (in heaven and on earth) which God the Father gave to Jesus in Matthew 28:18 was indeed a new kind of authority in relation to all creation because God has restored all things through Christ. This is evident in the other texts of the New Testament:
• 1 Corinthians 15:26-28 said that all things are not yet subject to the Father because all things are not yet subject to Christ. Christ gave the kingdom to the Father. The Father receives it. The Father subjects all things to Christ and then afterwards God became all in all. It was only after the Father subjected all things to Christ when it is said that God will be all in all.
• Colossians 1:19-20 said that all things have been reconciled to God through the blood of the crucified Christ.
• Ephesians 1:11 said that the time will come when all things will be under the headship of Christ.
Based on this biblical texts, it is possible for both God and Christ to have a authority over all creation due to the new relationship brought forth by them through the cross.