Apostolicam Ecclesiam: Tertullian vs. Turretin on the Church's Apostolicity

This will be the last post on the marks of the church, the fourth of which is apostolicity. After this, I will probably wrap things up with some closing remarks and analysis. Representing the Catholic side in this discussion will be Tertullian, writing at the end of the second century (The Prescription of Heretics, Ch. 32), and defending the Reformed position will be seventeenth-century theologian Francis Turretin (Institutes of Elenctis Theology, 18.13).

Here's Tertullian:

"But if there be any (heresies) which are bold enough to plant themselves in the midst of the apostolic age, that they may thereby seem to have been handed down by the apostles, because they existed in the time of the apostles, we can say: Let them produce the original records of their churches; let them unfold the roll of their bishops, running down in due succession from the beginning in such a manner that [that first bishop of theirs] shall be able to show for his ordainer and predecessor some one of the apostles or of apostolic men, -- a man, moreover, who continued stedfast with the apostles. For this is the manner in which the apostolic churches transmit their registers: as the church of Smyrna, which records that Polycarp was placed therein by John; as also the church of Rome, which makes Clement to have been ordained in like manner by Peter. In exactly the same way the other churches likewise exhibit (their several worthies), whom, as having been appointed to their episcopal places by apostles, they regard as transmitters of the apostolic seed. Let the heretics contrive something of the same kind."

And now here is Turretin:

"Falsely do our opponents maintain that the newness of our religion is gathered from the newness of those who profess it, such as Waldo, Wycliffe, Hus, Luther and others. They were not its authors, but only 'heralds and restorers,' who proposed no other doctrine than the prophetic and apostolic. It is one thing to purge an ancient doctrine of its corruption and recall men to it; another to devise a new doctrine not as yet delivered and propose it for belief. The former, not the latter, was done by the Reformers. They gave nothing of their own, but delivered what they had received from Christ. Hence the religion is not to be ascribed to them, but to Christ, who had taught it in his word."

A couple things should be pointed out. First, Tertullian does not ignore doctrine in favor of succession, but goes on and argues that the heretics' doctrine, "after comparison with that of the apostles, will declare, by its own diversity and contrariety, that it had for its author neither an apostle nor an apostolic man...." Secondly, the nature of Turretin's position is interesting because he is not simply arguing that the Reformed view is the most biblical, but that it is also the one that was represented in the early church. The claim, in other words, is quite demonstrable or falsifiable by an appeal to evidence (assuming, of course, that we are able to wade through the historical record with a measure of objectivity, but I digress).

So whose historical claim is right?