Good question. There is no price difference between attacking a player-owned district and an empty district. The price would be tied to what tier the district is, Poor, Comfortable, Industrial, Rich, or Aristocrat. 

[quote]x To attempt to claim a Poor district = 2 Wealth, 4 Personnel
x To attempt to claim a Comfortable district = 5 Wealth, 10 Personnel
x To attempt to claim an Industrial district = 7 Wealth, 14 Personnel
x To attempt to claim a Rich district = 10 Wealth, 20 Personnel
x To attempt to claim an Aristocrat district = 20 Wealth, 40 Personnel[/quote]

The one defending from the attack does not pay a fee. The only fee is the 'attempt' that the attacker has to pay. Of course, you're paying for the attempt, and it doesn't guarantee that you'll win. 

Does that answer it alright?