G'day Chad,
Essentially none.
The original Scots Reformed and the Continental Reformed were one in theology. Theology back then was a collective enterprise. The English visited and studied and taught in the Dutch and other Reformed centres, and many Continentals did the same in England and Scotland. The Scholastic style and Theology was shared by both British and Continental theologians.
It is easy to say that Puritanism, especially English, tended to be more devotional. But that is partly because we dont have a lot of Continental devotional works available in English. So the total picture is lopsided. Plus, many English devotional theological works were translated into Dutch and Latin and exported to the Continent.
One of the leading Puritans was William Ames. Ames was a key figure in early 17th century Reformed theology. Ames not only picked and diffused Covenantalism and the scholastic method, but he also had a strong devotional (casuistic) bent. Ames had also studied under Perkins, but later studied in Holland, and was at Dort. So in this period there was great cross-pollination; which even extended into the New World, as works by folks like Ames especially were highly prized. And on the other hand, the great Continental Scholastic Peter Martyr Virmigli studied in England until the Marian persecution forced him to flee.
Some examples: Great similarity can be seen by comparing Owen with Turretin on soteriology - the latter being more mature and balanced however. Owen's treatise on Biblical theology, however reflects a Covenantal Theology that was reflected by folk on the Continent. Francis Roberts, an English Presbyterian, wrote a massive work on Federal theology which is very very scholastic and very similar in style to Witsius, who wrote on Federal theology much later. Ball was another English Presbyterian who combined the Scholastic style with Federalism. It is argued that Ball's recently published work on Federal Theology was the text the Westminster Confession of Faith divines leaned heavily on.
Later American Presbyterian formed its own definitive character, especially under the influences of folk like C. Hodge, Dabney, and Shedd. But theologically, the American Presbyterians were one with the Continental Scholastics of the 17th century. For example, the later 17th century scholastic Turretin's Institutes formed the backbone of Hodge's theology, not only Hodge, but also Dabney and Shedd. When comparing Hodge and Turretin: the basic organising structures in the two systematics are identical. The differences are new issues and a new style of writing; which moved away from the scholastic method. With Hodge we have the new 19th century textbook method in Systematics. This style is replicated in AA Hodge, Shedd, Boyce, and even Dabney. Dabney was a very independent thinker and quite easily comparable to Hodge in calibre.
In Scotland, Turretin also was the theological backbone of leading lights like William Cunningham.
Confessionally, the differences are that the Anglo-American Reformed (i.e. Presbyterian) made the Westminster Confession of Faith (WCF) the prime subordinate standard, whereas the Dutch had the Heidelberg Catechism, the Belgic Confession and the Canons of Dort. These confessional statements were all written earlier than the WCF, and so therefore are not as theologically sophisticated as the WCF. But that does not mean that the WCF was deviant. The WCF theology is perfectly mirrored in later 17th century and early 18th century Continental Scholastics, like Turretin, a' Brakel, etc.
The areas of difference between Anglo-American Reformed and the Continental Reformed were mostly in matters of ecclesiology. One difference is life term eldership (Anglo-American) versus limited term elders (Dutch Reformed). This has been an ongoing difference for centuries. The Anglo-Americans tended to Postmillenialism, and so did the Dutch, while those under the influence of Turretin, etc., were Amillenial. This arose mostly in the later 17th century, and into the 18th and 19th. In the 20th, there seemed to be a reversal and Amillennialism gained ground.
The Dutch tended to presumptive regeneration. The English in the 17th century tended to presumptive non-regeneration. However, in the 19th century, under the influence of Hodge and Warfield, in the later 19th and early 20th centuries, presumptive regeneration came to the fore in American Presbyterianism. The Dabney-Thornwell line, which reflected the 17th century British view on this was pushed out of the foreground on this issue.
The American Reformed were more susceptible to the inroads of Fundamentalism from the 1920s onward, and often became narrow. The Dutch, however, were always a tad above fundamentalism and so were not so narrow in their outlook.
Also related to this was the Anglo-American Reformed commitment to an empirical Thomist apologetic - which was also the dominant mode in all the 16th and 17th centuries Scholastics (with the only highly debated exception possibly being Calvin himself). In Holland, however, Empiricism was never popular, after Decartes and Kant that is, and so under the influence of Abraham Kuyper, a non-empirical, non-Thomist approach to apologetics was developed, which has come down to us as Presuppositionalism. Those of the Hodgian-Warfield tradition tend to be Thomists, whereas those of the Kuyper-Bavinck position tend to be Presuppositional. Berkhof reflects the Kuyper-Bavinck tradition.
But also, apart from that, Berkhof reflects the Scholastic style incredibly, though this is merged with the early 20th century text book style, which makes for him to be an incredibly boring read. :-) That is to say, all his theological categories are incredible Scholastic to the point that to read him is to read the Scholastics (except for the Presuppositional angle I believe). Berkhof therefore is the child of the Scholastics but as mediated thru Kuyper and Bavinck. One can see both of these strains in his Systematics. With the well received antecedent rise of Presuppositionalism in the Anglo-American Reformed camp, Berkhof's Systematic Theology has received a warm reception. I doubt that had Berkhof's Systematic Theology been published 50 years earlier it would have been well-received in America or by American Presbyterians.
I have no idea - I am not an American and so am not familiar with these denominations. Hoped that helps.
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