I think there is a need for a clearer definition of what is meant by total depravity, and probably a separation of the term into two distinct terms. Both articles do this. There is total depravity in the sense of incapability to do good, which both articles affirm to be missing in the regenerate Christian, and there is the total depravity in the sense of depravity effecting every part of the human. These could be thought of as the depth and the breadth of depravity. Again, they both seem to hold that even in regenerate lives there is depravity of the same breadth, that is, we are still effected by sin in all parts of our being.They also both seem to agree that there is a lesser depth in Christians than in non-regenerate people, though still with non-zero depth until Christ returns.
The problem is that a total depravity person is defined as being a person who is depraved both as deeply and as broadly as possible, and Tchividjian is separating it to say that we are still totally depraved in breadth, though not in depth. The point that there are still residual effects of total depravity everywhere it has touched is well taken, but it might be better to refer to it as residual depravity instead of total depravity, since total depravity has established itself most thoroughly in reference to the depth of depravity.
If Total Depravity is defined as both breadth and depth, then Christians are not totally depraved. If it is defined as either depth or breadth, then we are, but definitions composed of or's cease to be especially useful. If we want to be clear in our theology, we ought to use clear definitions. While Tchividjian does define the aspects of total depravity that Christians still carry, his use of the term "total depravity" to characterize us is easily confusing, which I expect was what prompted the response by Phillips.
There is a further disagreement which Phillips brings up: whether we grow stronger when we grow in holiness. Well, what is meant by "stronger"? If it means, in both cases, that the amount of strength we have in ourselves increases, which is what I took it to mean in Tchividjian's article, then there is a real disagreement. However, if it is meant by Phillips to be our strength in God that is growing, then there is no contradiction between the two: God's power is made perfect on weakness, so it makes sense that the more we realize how weak we are on our own, the more Christ's power would shine in us. Not that we would necessarily find it easier to overcome sin, but that God's glory would shine more clearly. Whether that would satisfy Phillips, I am not sure. He makes a comment about Psalm 1:3
"Here is a picture of growth, strength, and spiritual competency. Yet it would be utterly wrong to say that this means such a person has become self-reliant at the expense of Christ-reliance."Which makes it unclear whether he wants to say that Christians are in some way self-reliant, or whether he is merely defending his view from the charge that it makes us rely less on Christ. If he wants to say that we can be stronger without relying less on Christ, then there is no necessary disagreement.