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From the Reformation Theology Site:

NCT is pretty much an in-house debate among (reformed) baptists and, the idea or system, I believe, has its roots in a reaction to legalism in some Reformed Baptist circles. Here are a couple of views they hold in contrast to Covenant Theology:

1) NCT rejects the covenant of works,

2) NCT rejects the active obedience of Christ. That is Christ’s full obedience to all the prescriptions of the divine law…making available a perfect righteousness before the law that is imputed or reckoned to those who put their trust in him.

3) NCT embraces only the passive obedience of Christ: Christ’s willing obedience in bearing all the sanctions imposed by that law against his people because of their transgression being the ground of God’s justification of sinners (Rom. 5:9), by which divine act they are pardoned.

4) So they (NCT) rejects the imputation of Christ’s righteousness to sinners being related to his having fulfilled the law. Rather the righteouenss he imputes to sinners is simply from the fact that he is God. So the emphasis is on his death and not on his life.

Wheras a covenant theologian would affirm Christ lived the life we should have lived and died the death we deserve, the NCT theologican would only subscribe the the second half of that statement. They would reject the idea that Christ fulfilled the covenant of works from our side. In our view (CT) this significantly downplays the necessity and importance of the incarnation.

Note: Whlie the above represent many within the NCT camp, I understand that it does not describe all streams of thought in NCT. Apparently some have moved closer to CT in these areas and differ only in that Christ having fulfilled the law makes the moral law no longer binding on the believer.