There are some who will insist that Systematics and Biblical Theology are complimentary and admittedly some Systematic theologians are better than others. And yet ultimately we return to basic questions - What is the Bible? What is the nature of revelation? How do we judge and interact with it? How did the Fall affect our intellect? And how do we faithfully understand and communicate what God has spoken? Is it our task to reflect Scriptural teaching even if it results in unresolved tensions and we are forced to limit some of our concepts - leaving loose ends and unanswered inquiries? Or is it the task of the theologian as Charles Hodge (1797-1878) argued - to treat the Scripture as something like data or a 'storehouse of facts' to be organized? The theologian's task consequently becomes something like a scientific discipline with the primary requirement being philosophical training.
The Church has long been forced to wrestle with so many of these issues and yet in the 19th century with the rise of new theologies, the seeming triumph of the Enlightenment and Scientific Materialism, the debates became more intense and for many the older Scholastic and Systematic approaches seemed insufficient. Redemptive-Historical Theology rose from amid these fires and yet in many respects it harks back to some of the earliest Christian writings. In the 20th century it was Reformed thinkers such as Geerhardus Vos (1862-1949) and Meredith Kline (1922-2007) who really helped to develop and apply this method. These men are both greatly appreciated and yet remain controversial in some quarters.
In the end, we often find that both methods bring us to similar locations. We often arrive at the same conclusions but (and this is critical) the means or the road by which we get there is quite different. And over time these differences do become more pronounced. Advocates of the Redemptive-Historical method will argue that it is able to better deal with nuance and subtlety while the Systematic approach is often blunt and rigid. The debate continues and seems all the more pressing given the commitment by some to culture war and other contemporary debates. As factions dispute the validity and ethical dimensions of war, some make a simple appeal to Joshua and David and argue that therefore America can wage war accordingly. A Systematic approach might (in some cases) lack the tools to make the necessary redemptive-historical distinctions, recognizing that not only is America not analogous to Old Covenant Israel, but that the New Testament has a different eschatological orientation. As citizens of the Kingdom of Heaven we are called to a higher ethic and thus the typology of Old Covenant Israel waging wars on its enemies was not an example for us to follow in our day, but a picture of Christ bringing future judgment. Obviously the implications are tremendous in how these issues are framed and how we live accordingly. As always, it's complicated.
The Redemptive-Historical method is less likely to result in what is commonly termed 'worldview' thinking. Worldview is akin to the Unified Theory (or Theory of Everything) that we hear about in scientific circles. For Christian thinkers this is ultimately a philosophical exercise as they seek to tease out (by means of systematic coherence and induction) a larger system of thought that moves far beyond the boundaries of Scripture.
Redemptive Historical approaches recognize the covenantal context of the Bible and how its promises are applicable to those who are in union with Christ and indwelt by the Holy Spirit. Worldview-ism seeks to apply the Bible universally (to those who are not in Christ) and as such it must develop theories of politics, economics, and culture in general - topics the New Testament does not address. Paul wasn't concerned with judging how the Romans lived (1 Corinthians 5:12). Redemptive-Historical theology reads the Old Testament in Covenantal terms and as such recognizes that it's poor exegesis to simply pull (ad hoc or even at random) from the Old Testament in order to fill a gap or solve some cultural conundrum. This is to fundamentally misunderstand the Christ-centered and covenantal nature of God's revelation and how it works. These issues are pressing to say the least and we've only skimmed the surface.