I can't think of a single reason why LeBron would pick NJ over NY. He'd have the same opportunities (money, talent of teammates, etc.) in NY and it's a bigger spotlight there.
Really?
Well, first the nets are moving to Brooklyn, so the spotlight thing is a wash.
Then, look at the team already in place at each spot. In order to be able to get 2 max players, new york would have to either sign and trade or renounce the rights to David Lee, McGrady, etc. Which means that the team he would have had in NY would be Lebron, the other max player, Curry, Gallinari, Wilson Chandler, plus a roster full of minimum salary players.
In the Nets, he'd be playing in Brooklyn with a team that has Devin Harris, Lopez, Lee, a top 4 lottery pick, and enough money left over to get close to a max player (or, they can trade Harris for one of the other max free agents).
Any way you cut it, he'd have a much better supporting cast with the nets than in NY.