The problem with fractional_even is that you get a very tight mass of triangles mid edge, and very large triangles in the corners. Obviously this has potential for artifacts. With fractional_odd this difference is much less pronounced. I'm not sure where anyone would ever want to use fractional_even unless you had very specific topology that benefitted from that imbalance somehow. Here are some wireframe results:
fractional_even:
[attachment=15320:PartitioningEven.jpg]
fractional_odd:
[attachment=15321:PartitioningOdd.jpg]