The new rules do share a similarity with the old rules. The first $600,000 in gains aren't taxed. However, the old "10-year rule" is gone. Additionally, if an individual who renounces his or her citizenship later gives a gift or an inheritance to a US resident, that gift or inheritance will be taxed at 45%.
If you plan on, or are considering renouncing your citizenship you absolutely need to discuss your situation with a tax accountant and an attorney. If you're wealthy, just plan on leaving some of your money to the Internal Revenue Service whether you want to or not.
Other Coverage: Don't Mess With Taxes