I have been asked many many times over the years how Evangelical Calvinism is different than classical Calvinism (i.e., Federal theology, 5-point Calvinism etc.). There 
are a few ways to try and answer that; but an important way is to signal the type of theological methodology we follow (contra the competing traditions out there). Us, Athanasian Reformed look directly to Calvin—unlike the Post Reformed orthodox, ironically—in order to distill the various themes that help fund what we are attempting with this project.
As Providence would have it (Christ conditioned Providence, that is), I am rereading John Webster’s little book (one of my faves) Holy Scripture: A Dogmatic Sketch. In the following he sketches the spirit of Calvin’s theologizing. In his sketching what ends up being revealed, to an extent, is what characterizes the way us Evangelical Calvinists intend to operate. Webster writes:
Calvin is, of course, a scriptural rather than a speculative or systematic theologian, fulfilling his office as doctor of the church primarily through his biblical lectures, commentaries and sermons. The Institutes is no exception, for its purpose is, as Calvin puts it in 1559, ‘to prepare and instruct candidates in sacred theology for the reading of the divine Word, in order that they may be able both to have easy access to it and to advance in it without stumbling’. But the principles which underlie Calvin’s intense engagement with Scripture are distinctly theological: Scripture is the lode-star of his work because of what he sees as its place in the divine work of salvation, above all, its functions of announcing the gospel, reproving idolatry and fostering true piety. And there is a direct consequence here for the reading of Scripture: what is required of the reader is not simply intellectual skill, but above all a certain brokenness, from which alone truly attentive reading can follow.[1]
So, us Evangelical Calvinists are, in fact, rather Calvinian (versus, Calvinist) when it comes to our ressourcement of Calvin’s teaching; we do so constructively. Calvin, surely, was a product of his time; but he was also trailblazer, in the sense that he was much more Christ concentrated in his approach than many of his contemporaries. Like Calvin, Evangelical Calvinists are radically committed to the Protestant ‘Scripture Principle,’ and a radical Theology of the Word, to boot. Like Calvin, we reject the “schoolmen’s” deployment of scholastic methodology.[2] We aren’t prone to Lombard’s Sentence-like theology. We think Thomas Aquinas was a deeply entrenched Roman Catholic with very little to nothing to glean from (the late Webster disagrees with us there). We aren’t fans of applying Aristotelian categories to the exegesis of Holy Scripture. And we, like Calvin, reject the intellectualist anthropology that funds the whole superstructure of Latin theology; whether in its Catholic or Protestant iterations.
Webster, rightly leaves off with a final note, with reference to Calvin: “what is required of the reader is not simply intellectual skill, but above all a certain brokenness, from which alone truly attentive reading can follow.” As Webster underscores, Calvin had a theology of the cross funding his approach to Scripture. Calvin understood that the true theologian must be one who is fully dependent on listening to the Redeemer’s voice; that is, if an intimate knowledge of God was ever going to obtain.
[1] John Webster, Holy Scripture: A Dogmatic Sketch (Cambridge: Cambridge University press, 2003), 74.
[2] To be sure: Calvin was still the son of late medieval categories, so those are apparent in his personal theological grammar. Yet again, this is what makes Calvin so special for his time: i.e., he wasn’t a slave to his own period—I’d argue because he was first and foremost a slave of Christ, to the point that this affected his theological prolegomenon in more “relational” or “personalist” ways.