Systematic theology is far too restrictive and limiting for God to operate within its prison walls, so He politely excuses Himself from the penal institution of religious dogma. Systematic Theology is a lens through which the scripture is read, obscuring certain truths, while enhancing others, and thereby creating half-truths that become lies, and partial truths that exaggerate some truths and minimize others, thereby making a caricature of the God of the Bible.
Though it is certainly not the only example, the clearest example of this, to me, is Reformed Theology, and more specifically, Calvinism. Calvinism has made a caricature of God and His nature with some of its clear truths of soteriology, the perverted and therefore misapplied doctrines of sovereignty and election, and the minimized or overlooked passages that do not comport with the tiny box of theology created primarily from its grand overemphasis of a single chapter of a single book of the Bible: Romans chapter nine.
Biblical theology allows the scripture itself to state its own creed. It doesn't make a statement of faith or doctrine (dry wineskin) and then cherry-pick scriptures to buttress a perspective so highly engineered that it cannot expand without threat to its structural integrity from the life of God that ever moves and expands, ever conquers and deepens, yet without change or variation. The mustard seed of scriptural truth contains the DNA of the fully grown and developed that is in essence consistent, but in personal revelation, always growing and expanding, bringing the leaven and the light of the kingdom into the heart and mind of the individual who, having been divinely instructed, rather than instructed of man, never has to forsake "old truths" in order to grow in the knowledge of God (1 Jo. 2:27).
When Paul had penned some of the deepest truths of scripture in the most systematic development of truth ever laid before the eyes of man, because he wanted his brethren to "understand this mystery" (Rom. 11:25), he then gave the key to theology - "O the depth of the riches both of the wisdom and knowledge of God! how unsearchable are his judgments, and his ways past finding out!" There are some things that we cannot know while we know in part. Some of the mysteries of the Kingdom are given to us to know, but others are given, if you will, in parables that may tend to obscure the truth that is too wild to be tamed by the theologian's whip or chain.
Systematic theology is man's creation, and though it may contain truth, it can never BE truth. In fact, ultimately, it can only limit a man's view of the truth. A person that submits themselves to a man's theology allows that man, as a mediator, to seal him in the forehead, and that seal often allows no entrance to greater or divergent truth, even, tragically, truth directly expressed by the Spirit of Truth. Biblical theology allows the living and organic eye of man's spirit to view far and near with the oversight of spiritual maturity, but the monofocal, or bifocal lens of systematic theology will blur as well as it clarifies, and obscure as well as it reveals, leaving the picture grossly distorted or lacking, and leaving the student blinded to the grand vista of truth in all its polychromatic grandeur.
Systematic Theology is man breathed, but all scripture is God breathed, and profitable and able, and the sum of His word is truth (Ps. 119:160 ASV), not the isolated addends, in that some of these addends, standing on their own, do not express or represent the sum. The word of God is living and active, and to divide something living is to kill it. Systematic Theology, by its nature, carves off some and preserves other truths, making a dead thing from that which is living; the word of God. Biblical theology recognizes that some things we don't know, for we know in part, and it allows the living word of God to speak for itself, even in realms where we have not ventured in practical experience or personal understanding. So, I believe that, as I have used the term here, biblical theology is the theology of more noble men than those who hold to a systematic theology. Further reading on biblical interpretation: http://buildinghishouse.org/believe/interpretation.shtml