Covenant Theology has a high view of the unity in God's purpose in human redemption. It is called "covenant" theology not because of an emphasis on the Biblical/historical covenants as such but on certain theological covenants -- the covenant of works (Gen 2:16,17), the covenant of redemption (a necessary precursor to Gen 3:15), and the covenant of grace. The covenant of grace is essentially the promise made in Gen 3:15 of the coming deliverer, and all of history is viewed as a progressive unfolding of this covenant. Thus, the New Covenant, in Covenant Theology, is not understood as a new covenant actually; it is rather a new administration (or dispensation) of the covenant of grace, as was the Mosaic Covenant before it. One covenant with various administrations is the essence of Covenant Theology on this point. Therefore, the Old Covenant is seen as an essentially gracious covenant, not a legal one. Further, with this emphasis on the unity of God's purpose there is a strong tendency in Covenant Theology to carry over the old order into the new: the church is the Israel of God, the law of circumcision in the Old Covenant is intimately linked to the baptism of the New Covenant.
Dispensational Theology emphasizes rather the various differences in God's dealings with men. A "dispensation" has to do with the various administrations of Divine truth. With new revelation come new responsibilities and/or privileges. This change results in a new "economy" or dispensation. With this emphasis on the various changes in God's program, Dispensationalism sees more emphasis upon the differences between the old and new economies or dispensations. For the (traditional) dispensationalist, there are two separate peoples of God running through all history and even eternity (National Israel and the New Testament Church), law is a thing of the past and largely irrelevant to the New Covenant believer, and so on.
Blessings,
msortwell