What is the difference between 'Biblical' and 'Systematic' theology? Particularly among Protestant traditions, it is common to classify books and classes that cover broad looks at theological issues as either 'Biblical' or 'Systematic'. Sometimes this is even extended to categorize theologians.

What is the difference between these arrangements or systems? Are they in conflict or competition with each-other, or are they complimentary in some way?
Biblical and systematic theology are two different ways of studying the Bible.  The main difference is what the theologies study.

Biblical theology is focused on studying a portion of the Bible and how that relates to the rest of the Bible.  An example may be specifically studying a portion of Isaiah.  The person studying may look back at what led up to one of Isaiah's prophecies and how that prophecy is fulfilled in Christ.

Systematic theology focuses on different topics and studies what the Bible says about that topic.  An example here may be studying the attributes of God.  A person studying the attributes would start by finding all the scripture which mentions the attributes of God.  After having all the scriptural references, they could then build a doctrine based on that scripture.

These methods of theological study are complimentary.  While biblical theology may give you insight into a specific portion of scripture, it may not be the best way of building a doctrine since it may not give you all that scripture says on a specific topic.  On the other hand, systematic theology can give you a very detailed view on a topic, but that view can be enhanced by providing even more context to the specific scripture which discusses a view.