The molybdenum version is most common in nature, and used preferentially in organisms that possess it. It has also been studied the most. No known organism possesses either of the other two versions while lacking this one. Protein sequences of this enzyme in different organisms are remarkably similar to each other. It uses 2 ATP to transfer one electron from the dinitrogenase reductase protein to the dinitrogenase complex, and 6 such transfers reduce one dinitrogen to two ammonia (along with 2 electrons going to hydrogen).
The other versions were discovered when Mo or its enzyme were unavailable yet nitrogen fixation continued. They have an extra subunit of unknown function (perhaps cofactor insertion), but otherwise seem pretty similar in structure and function.
Other than those three, Streptomyces thermoautotrophicus has a novel system: it has Mo in the dinitrogenase and the dinitrogenase reductase equivalent is a manganese-superoxide oxidoreductase with no iron or sulfur. It doesn't do acetylene reduction, but far from being oxygen-sensitive, it depends on oxygen for its activity. The overall stoichiometry is similar to the Azotobacter Mo nitrogenase though, including the hydrogen production, but the minimum ATP requirement is only 4, instead of 16.
Then the authors go into some discussion of other nitrogenases, with the same apoenzymes as those in A. vinelandii but with different central cofactors that may or may not be found in nature. For example, a tungsten-iron cofactor, which has been studied before: it doesn't permit nitrogen fixation, but some proton reduction is possible. Then there were chromium- or manganese-iron cofactor proteins: when extracts were treated with o-phenanthroline and purified as apoproteins, activity could be partially restored with solutions including salts of Mn, V, Mo, Cr, or Re. W failed to give this effect, but the others permitted some acetylene and proton reduction activity. I don't have access to the citations for these claims though.
These in vitro proteins, even if they contain weird metals, also seem to contain Mo in equal proportions to the others. A. vinelandii UW3 lacks nif genes required for the primary nitrogenase, but can use alternatives, and some suggest that the V nitrogenase may use Re or Mn or Cr instead; or maybe the Mo nitrogenase proteins are expressed but use these metals. It doesn't seem very clear, but it's interesting.