What is the difference between an Old Testament saint and a New Testament saint? How does the Gospel of the New Testament differ from the Gospel of the Old? These are worthwhile questions, and we wouldn't want to overlook them. Here are a few of my [incomplete] thoughts, based on Scripture:
Old Testament saints were justified by faith alone. This is the doctrine established in Romans 4, based on Genesis 15. This is essentially the main point of Romans 4:1–5, that justification by faith alone is not a new doctrine. And so the chapter begins with an appeal to the Old Testament record of Abraham, "What shall we say then that Abraham our father according to flesh has found?" (Romans 4:1). God has never justified anyone on the basis of anything other than faith.
Old Testament saints had forgiveness of sins. This, too, is the plain teaching of Romans 4, based on an appeal to Psalm 32. Romans 4:6–8 establish that David was a man "to whom God shall not at all reckon sin" (v. 8). This is an interesting statement, because in many ways Christendom has actually fallen lower than the Old Testament saints. Where David said that God would "not at all reckon sin" to him, Christians today seem to believe that sins they have have not confessed are reckoned to them. Of course this essentially means that God forgives based on works: confession becomes meritorious in this twisted theology.
This comes from confusing God as Father with God as Judge. We can (and do!) confess our sins to our Father (1 John 1:9), but we don't confuse that with our standing before God as Judge. Acting inconsistently with my place as a son of God might strain our relationship: it might make it difficult for me to enjoy Him and His company... but it doesn't in any way change the fact that God is my Father. A disobedient son is still a son. The Old Testament saints were children, but they weren't sons.
Old Testament saints were born again. I think a lot of people miss this, but it is what the Lord Jesus specifically taught. Consider His words to Nicodemus: "Except any one be born of water and of Spirit, he cannot enter into the kingdom of God" (John 3:5). No one can get into the Kingdom of God without being born again; but "Abraham, Isaac, and Jacob" (Matthew 8:11) will be in the Kingdom, along with "all the prophets" (Luke 13:28–29). So we can be sure they were born again, can't we?
To take it even further, the Lord Jesus told Nicodemus he ought to have known about new birth, because he was a "ruler of Israel" (John 3:10). So the need for new birth was a truth the Lord Jesus expected a "ruler of Israel" to know, presumably based on the Old Testament. Johnny D. suggests this is an allusion to Ezekiel 36:25–31. Perhaps this is the portion the Lord Jesus was thinking of, but regardless: it's clear He considered the new birth to be Old Testament truth.
So if the Old Testament saints were born again, if they were forgiven of their sins, if they were justified by faith alone; what is the difference between the Old Testament saints and the New Testament saints?
The Holy Spirit wasn't given in the Old Testament. John 7:38–39 explicitly state that "the Spirit was not yet, because Jesus had not yet been glorified." Of course we don't understand that to mean the Holy Spirit did not yet exist! That is clearly untrue, because He was there at the creation (Genesis 1:2). Of course the Holy Spirit existed, but He was not yet given. The giving of the Spirit was dependent on the exaltation of Christ, and Peter used the manifestations of the Spirit on earth to prove the exaltation of Christ in Heaven (Acts 2:33–36).
The New Testament saints have "no more conscience of sins." Hebrews 10:1–5 contrasts believers in the New Testament with the Old Testament saints under the Law. The first point of contrast is that the Old Testament saints did not have a once-for-all sacrifice for sins. Instead, they had repeated sacrifices. Those sacrifices reminded the people over and over that they had sinned. But our High Priest has offered One Sacrifice forever for sins, and so we should have "no more conscience of sins" (v. 2). Of course, I don't think this is very clearly taught or very clearly believed in Christendom as a whole: but the truth of the New Testament is that we have "no more conscience of sins".
Old Testament saints were justified looking forward to a future work: we are justified looking back on a completed work. This is the teaching of Romans 3:21–26. In the Old Testament, God justified men and women who believed Him, looking forward to the payment He knew He'd receive from Christ. But now that Christ has actually died, been buried, been raised from the dead, and ascended into Heaven; God justifies us based on historical fact. That doesn't mean we're any more justified, but it does mean that we are conscious of what the Old Testament saints couldn't know. And this is what Romans 3:21 says: what the Law and the prophets bore witness to, we now have manifested. There is, in a sense, an advantage to us, because we have the privilege of seeing what God foreknew. We have, in this sense, a more complete view into the heart of God than they did.
The Old Testament saints did not have the adoption of sons. This is the whole point of Galatians 4:1–7. The Old Testament saints were children of God (cf. John 11:52), but they weren't sons. Sonship is different from childhood. A child, Galatians tells us, differs not at all from a slave (v. 1), but the Lord Jesus came so that "we" could receive sonship (vv. 4–5). Sonship is characterized by a close relationship with the Father. It implies familial rights, it implies a claim on the Father. The Old Testament saints didn't cry "Abba, Father" that requires the "Spirit of His Son" (v. 6). Galatians 4:1–4 agrees with John 7:38–39, the Spirit of God couldn't have come here until the Lord Jesus' death, burial, resurrection, and ascension (1 Corinthians 15:3–8).
I'm flagrantly ripping off Johnny D. here, but this is a huge point. The spirit of adoption is characterized by a confidence in God as Father. Servants don't have confidence in God as Father: they might love and respect God as Master, but they don't have the confidence in the Father's love. This is a new thing: this began in Acts 2 when the Holy Spirit descended.
The Old Testament saints were not united to Christ. The New Testament saint has been united to Christ in His death (Romans 6:3; Colossians 3:3), His burial (Romans 6:4), and His resurrection (Colossians 3:1). The Old Testament saints we not. The Lord Jesus said that there could be no union with Him until He died (John 12:24). We feed on Christ as dead (John 6:53–57), we eat His flesh and drink His blood: you can't do that unless He has died.
Now, this isn't a complete list. But it's something I've been thinking about recently, and discussing with friends. I thought it would be worthwhile to post a few of those thoughts here.