The prepositions used by Paul in the question are the same, in relation to justification, as he uses in Philippians 3:9 :
And be found in him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith: Phiippians 3:9 [KJV]
Here, Paul emphasises that justification is a matter of the righteousness of God. The righteousness wherewith men are justified is God's own righteousness.
And as he says previously in Romans :
For therein [in the gospel] is the righteousness of God revealed from faith to faith Romans 1:17 [KJV]
By the revelation of God's own righteousness (demonstrated in the sufferings and death of Jesus Christ, his own Son) and by faith in that demonstration, men are justified.
But it is also through the faith of Christ himself in offering up himself.
The agency is through the faith of Christ.
The means is by the faith of the believer.
Thus in Romans 3:30 Paul emphasises that the believing Jews are justified by their own faith, not their previous works, these works being immaterial to justification. Paul emphasises the means of believing, as opposed to the useless works of the flesh.
Whereas Paul emphasises to Gentiles that justification is through faith (that is to say the faith of Christ) and thus draws attention to the grace of Christ in reaching even to the far off Gentiles who had no means at all at their disposal to draw near to God. Thus Paul emphasises the agency of Christ to the far off gentiles.
