1. New York people have more ambitions in their 20s, but less in their 30s than people in Austin. People in Austin seem to be late bloomers more so than the super hungry, overachieving types that land in New York in their early 20s. That said, the New York people usually get tired around their early 30s and slow down (and get jaded, having been passed over for promotions or watched as others were "winning") while Austinites seem to pick up steam personally and professionally as they become more in touch with themselves overall through a mixture of earlier disappointment, introspection, and sheer maturity.
2. Austin people are less culturally-motivated than New York people. They have fewer minority friends, fewer friends living around the world, fewer friends succeeding in diverse professions, etc. But but but...Austin people attain their cultural awareness through personal interests moreso than New York people, who primarily get their culture through professional interests and relationships. This is an important distinction because when New York people move to Austin, they are likely to feel the need to continue traveling (for work or play) to get their cultural fix, whereas Austin people who (later in their 30s) become more professionally motivated choose to move to cities like New York where the cultural assets and connections are already built in.
3. The end of being "young" in Austin is somewhere around 31 years old. The end of being "young" in New York is somewhere around 36/37. I'm not saying I personally agree with this definition - I think there are droves of people in Austin and New York who are much older and still quite young - but that's what I've observed based on who my friends are in these two cities and what they get into.
In Austin, if you're a 36-year-old guy, you're probably married so you look forward to ACL Festival (where you either paid for a VIP pass or got one from a friend at C3) in the same manner a 36-year-old guy in New York (likely still unmarried) looks forward to a trip to Art Basel in Miami or Sundance Festival where you probably have media or VIP access through your job or mutual friends.
Again these are gross generalizations for the point of sharing some thoughts I have on the two cities.