I know that the two organisations work very differently behind the scenes but as some one else here mentioned, they're both content aggregators at their core. And let's be honest, if a story is on one news website, it's on all of them so it's not like the NYT is a special place that has all the news no one else has.
There's a lot of reasons why reddit gets much more traffic, but I genuinely believe the way they present their content is more accessible to more people, and that's why they can so successfully grow and retain their user base, and I think that's why simple list presentations consistently win out over complicated presentations. Flip book might be a more sensible comparison, that's an aggregator and it's a bore to use after a while.