If it seems like Topsy Turvy to have Manhattan rents sink while Brooklyn rents rise, it's not all that hard to understand : quite simply, when two things are considered equal, prices reach a similar level. Given that many people now work in Dumbo and Williamsburg, or just across the river in Lower Manhattan, it's not too hard to equate the lively Brownstone neighborhoods in Brooklyn to the charming Landmarked areas in the Village, Soho and Tribeca. So rents in the two areas are meeting each other.
The article somewhat contradicts itself by saying that tight credit markets (making purchasing homes harder) hold renters in place, but that Manhattan rents may have gone down because many purchased. I say that the more likely answer is that people now see Manhattan and parts of Brooklyn as interchangeable and live where they find the most personal value in doing so.