Of course Knicks are much more relevant in New York but when it comes to building a team this does not really matter all that much. Nets have great scouting, the players they have picked up through draft have all outgrown their position in the draft (LeVert, Allen) or look like they will (Kurucs), they've picked some very solid cheap talent (Dinwiddie, Harris) and will have lots of cap space. They don't have to go for the top tier of talent, if they can dig into that second tier and get someone like Tobias Harris or Middleton then they will be well equipped to become a solid playoffs team with potential to do more. Russell has been absolutely INCREDIBLE for them recently as well.
As for Zion, if they get him (again, 14% chance that they do), I suspect they will be trying to flip that for Anthony Davis still. I don't think they should but if they feel getting AD will get them KD then they will do that, however I think having a prospect of playing with Zion, Porzingis and a nucleous of talented young players - plus possibly getting another good free agent - could also be appealing to KD or other big free agents.
Zion is immense though, I think he may be one in a generation kind of talent. I'm sure Pelicans would love to get him for AD, it's the best possible scenario for them because they get someone who instantly brings attention to the franchise. Even though Tatum is more NBA proven, his marketability is not at that level. Whoever gets no. 1 pick will have a shot at getting AD but I think only Knicks would actually try.