I believe the Old Testament saints wanted direct communication with God,at least some of them,for anybody that wants to abide in the truth of God will want a relationship with Him,for they want to do right,and David was a man after God's own heart.
The Old Testament and the New Testament are no different for salvation,as long as the people in the Old Testament repented of their sins,and the blood of animals covered their sins,for then their sins were washed away by Jesus,and a saint like all the New Testament saints,and no different.
The 12 tribes of Israel are written in the New Jerusalem,and the 12 apostles of the Lamb are written in the New Jerusalem,and there is no saint other than that written in the New Jerusalem,not even Paul with all his writings,and reaching out to the Gentiles.
To me they seemed like more honorable men,with greater impact in the Old Testament.
The Old Testament and New is different in this.
The Old Testament was given that had the moral laws,laws of love,but they could never live up to them perfectly not having the Spirit,and they could not be spiritual,so God had them physical ordinances that they were able to keep,until Christ came.
Also God allowed them to war against their enemies,and they had material,and monetary blessings,which are not applied in the New Testament.
Jesus said a new commandment I give you,that you love one another as I have loved you,which they can do by the Spirit,and preached a more excellent way of love.
In the New Testament we only go by the laws,love God,and love people,moral laws,and abstain from fleshy pleasures,and do not eat an animal with the blood,or has been strangled,for that is still in effect,for do not eat the blood,for the life is in the blood.
Jesus took the physical ordinances of Israel out of the way,nailing them to His cross,for they had no benefit for spiritual salvation.
Sin separates us from God whether Old Testament,Jew or Gentile,or New,confess Christ,or not confess Christ.
If we do not want sin by the Spirit we can abstain from sin,for that is what God wants for us to abstain from sin.In the Old they could not do it not being able to receive the Spirit,and in the New we can do it by the Spirit.
But salvation is the same whether Old or New,and no difference there,for in the Old,the blood of animals,Christ came washed away their sins,and in the New sins are washed away,and are a saint either way and with Jesus.