ASSASSINS was a special case (one that required the deliberation of the Tony nominating committee). Although it never premiered on Broadway until 2004, by that time it had already played in regional theatres around the world. It was well-known and oft-performed, so the committee considered it a "classic."
By contrast, FALSETTOS (being made up of MARCH OF THE FALSETTOS and FALSETTOLAND) was still considered for the Best New Musical (and Best Score, etc.) Tony, even though MARCH OF THE FALSETTOS had opened over ten years prior, because the piece had only been performed in a tiny handful of theatres in the country and was not yet a "classic" (this is a bit anachronistic of me to say, because the committee's deliberation on this subject only began last year).
BlueWizard's blog: The Rambling Corner
HEDWIG: "The road is my home. In reflecting upon the people whom I have come upon in my travels, I cannot help but think of the people who have come upon me."