It is not like Civ4 where many players can be building a Wonder at a time, and only one gets to keep the finished version.  Starting building a Wonder first puts a block on any other player building it, *while in remains in your queue*.  In my game I build a Fort or something instead of a Great Mill because it was quicker and when I came to build a Great Mill it wasn't an option any more.  Then I found out 5-10 turns later Gilden had built the Great Mill.  So I am very certain that it is the first player to start a Wonder that gets to keep it, provided they continue building it.  This might seem too easy, but Wonders take a lot of production and if you stop production then another city can get to build the only version, but building the Wonder may prevent you from building other needed buildings.  So I think it is a good tradeoff.