How does second edition farmer scoring work?
A city can be scored once per player, so in the given example, each player would receive 3 points.

I found the answer while combing through some threads on boardgamegeek.com, as well as in an answer to this other question.

From the other answer:


  A player can score for a single city one time, and only one time... no matter how many fields and farmers he has next to it.


And from bgg:


  German 2nd Ed:
  1) look at each city
  2) if a player has the most farmers in any one of the 
  fields adjcent to the city he scores 3 points.


So it appears that while second edition does consider each field separately; it still scores city-by-city, as opposed to scoring farm-by-farm, and for each city multiple players might score the 3 points.