Funny you should ask, I had this piece on Bleacher Report this week exploring that very question.
The short version is that the dynasty is over because this is a totally different team, but there’s no question they are still one of the best teams in the NFL. If/When they win another Super Bowl or two it would have to be considered separate from the first dynasty with the only connection being Belichick/Brady.
But there’s no question New England is a model franchise, and have continued to win despite near completely new personnel between now and 2004.
To break it down simply, 2001-2007 was the dynasty. 2008 was a transition year, then 2009-present is the second act of the Belichick/Brady reign.