ESPN just posted an article (an AP story actually) that is the best breakdown of the new collective bargaining agreement that I've stumbled upon so far. It seems that draft pick compensation hasn't totally been done away with:

Draft-pick compensation for losing Type C free agents is eliminated. Compensation for Type B free agents is changed from direct (losing draft picks) to indirect (sandwich picks). Starting in 2007, Type A free agent redefined to top 20 percent at position (from top 30 percent) and Type B to 21-40 percent (from top 31-50 percent).
Thresholds for luxury tax on team payrolls set at $148 million for 2007, $155 million for 2008, $162 million in 2009, $170 million in 2010 and $178 million in 2011. Tax rates on amount over threshold remain at 22.5 percent for first time over threshold, 30 percent for second time over threshold, 40 percent for third or subsequent time over threshold.

Now, this still doesn't answer the question of whether teams would now revert back to "first-time offenders". This would only affect the Yankees but it's a noticeable effect. Rather than paying a $1.40 for every dollar spent over $148 million, they would pay $1.23. If next year's payroll was the same as this year, you're talking about a little over $8 million bucks that would stay in the Yankees' coffers. (Though between Moose, 19M, and Sheffield, 13M, there's going to be some dropoff next year.)

Update: According to Peter A., the Yankees will remain at the 40% level as a repeat offender. They will be the only team over the salary cap.

As an added note to you minors watchers out there, the new CBA also states that players in the minors now have four full years before they have to be added to the 40-man roster or exposed to the Rule 5 draft. It used to be three years. That's helpful for all the Yankees prospects at the lower levels.