To be clear, what are your definitions of each? While I think we can all agree on what the old left is, I think the New Left might be a foreign concept to some people. The New Left certainly isn't centrist or at all involved in politics today.
To me, the New Left was a political movement in the 60s and 70s. It was about moving away from actual political organizing and labor organizing and into social movements like anti-Colonialism, feminism, anarchism, gay rights, radical environmentalism and various forms of critical theory. I think the legacy of the New Left is feminism and gay rights acceptance in the US, which is good. But, legacy of the New Left is mostly negative because it moved left-wing activism into this insular university niche of focus on academia and the personal lives of a few intellectuals. That basically guaranteed that the left would fade from any influence because politics is about power, not sitting around at Berkeley writing poems about how terrible anyone with power is.
This.