This is something I've been thinking more & more about. Didn't realize there were some names for the posting styles that can be involved (POSSE/PESOS), so that's interesting.
One of the parts that I don't think some folks take fully into account with the first method (post on site, syndicate elsewhere) is how if done poorly it can easily put people off, as it becomes really obvious you're basically just broadcasting rather than trying to really talk to people or start conversations in their own spaces.