As to the distinction between dogmatics and ethics, dogmatics is the branch of theology that outlines what we believe, whereas ethics focuses on the Christian life (how we live according to God's law).
I haven't read Bavinck front to back (just vol. 1 and portions of the other three). Truthfully, I haven't read the Institutes yet from front to back either (working on it). But I think I'm familiar enough with both to comment. Calvin was not writing a systematic theology in the sense that we understand it today. The Institutes was a book to help people prepare to read and understand the Bible. Bavinck's RD is more like a systematic theology, progressing through all the typical topics. Bavinck was written mainly for theologians and budding theologians (seminary students). Because he wrote later, Bavinck is also interacting with theologians of the 19th century, something Calvin obviously couldn't do. Also, because he writes later, Bavinck is also working within the framework of the Reformed confessions, particularly the Three Forms of Unity. He often referred to the TFU and was committed to these confessions. You'll also find that Bavinck's covenant theology is much more developed than Calvin's, simply because so much water has been under the bridge between the two.