Are the apostles equal to Christ in authority?
teaching authority
Why do you ask only about the apostles? Christianity tells of the reason for Christ's sacrifice is that everyone who believes in His name should become a child of God (John 1:12) and a co-heir with Christ (Romans 8:17). But I know that does't answer your question, and I think that the answer to your question is that nobody can really be a replacement for Jesus Christ, but that the hope of God is that we might grow into all ways to become like Him (Ephesians 4:15).
In that passage of Ephesians 4, St. Paul writes that each of us is part of an overall corporeal body that is the spiritual body of Christ, and in that way he explains that while one may have a particular function in the body of Christ, we can't very well say to each other "I don't need you" - just as an ear may feel that it can function perfectly fine without the eye.
He even goes so far as to say that when one part of the body suffers, the whole body suffers and when one part is glorified, the whole body rejoices. So it is clear through an analogy like that, that there is definitely differences in the scope of function of each person in the body - while one may have a strong talent in teaching, and they might be considered an authority on doctrine, another may be gifted in the healing of others - and yet it is not as though a teacher will never be gifted to heal or a healer be required to teach. Indeed there is clearly some inter-dependency of the gifts in Christ, and that is what we see in Jesus Christ: that He was exercising the whole nature of Christ to the fullest human extent. When He said that we would do greater works than He, it is His clear vision of hope that His body would go throughout the whole earth and bring healing and teaching to redeem the world from eternal destruction. But about the authority of Christ in each one of us, you really need to think differently about what authority is, because authority only matters when that authority is demonstrated by power and I'll tell you why authority isn't necessarily the same as power, it is because although the one who has authority commands the power and it acts, the power itself is the one who believe the authority has the right to command its obedience. If the power decides to rebel against the authority then the authority really has become powerless and therefore is effectively not an authority. So where is the authority in Christ? You know it is not through the right to command power, but it is through trusting in God's power to bring about justice and to save. Therefore it is not the one who claims the authority that is powerful in Christ, but the one who trusts in God to endure persecution when it arises. God's way is to bring low that which exalts itself and to raise up that which does not dominate. There is no other way to bring about salvation through the rights and authorities and powers that belong to the kingdom of God.