I had the pleasure of listening to most of Yesterday's Baptism between Dr. White and Mr. Strawbridge.
1) I don't think that Dr. White was consistent in his exegetical method. Dr. White (it seemed to me) insisted that we have to read the New Testament first, and then go back and read the Old Testament. Normally, however, Dr. White would encourage people to read the writings in the order they were written. Dr. White himself set the bar that if he uses different methods on this doctrine than other doctrines, he is imposing tradition on the text. With respect, I think he may have fallen afoul of his own standard in this case. Possibly, though, I simply misunderstood the argument he was trying to make.
2) Dr. White made much of the fact that the new covenant is "not like" the old covenant, and that the new covenant is better than the old covenant. Dr. White seemed to suggest that this difference was faith, with the implication - not always made explicit - being that only those with faith (evidence of regeneration) should be given the sign of the new covenant.
This argument has several flaws.
a) The difference between the old and new covenant is in the priesthood and sacrifices in the context of the passages upon which Dr. White relies;
b) Faith is not the difference: for Abraham was circumcised after faith, just like first generation believers under the new covenant, and just like old covenant proselytes; and
c) Circumcision and Baptism picture the same thing, the work of the Holy Spirit in the heart, but the recipients of circumcision were not necessarily regenerate; nevertheless they were given the sign of the covenant.
I listened with a number of sola-credo-baptists (or anti-paedo-baptists - or simply "baptists"), who seemed to think that Dr. White's point about "not like" the old covenant was a very good and very strong argument. I didn't really see why they thought it was strong. In fact, I'm going to listen to the debate a few more times to see if I missed something, because it seemed quite weak to me.
3) Mr. Strawbridge started well, but did not really seem to be able to concentrate and make good use of his time during the debate. Unfortunately, he got distracted by his cell phone going off mid-debate, and lost track of his allotted time. He made a few good points, but as far as debating ability goes, I really feel he was outgunned by Dr. White. Dr. White spoke significantly faster, and focused much better.
Also, it was suggested to me (by the folks I was listening with) that Mr. Strawbridge may be part of the "Federal Vision" (FV) movement. If so, of course, that would be a reason for me to distance myself from Mr. Strawbridge's presentation, as the FV movement has some questionable views when it comes to the issues connected with the sacraments.