On the new screenshot you can see the identical curve placed in two different locations on the sphere. The copy on the side of the sphere does not exhibit the strange behaviour of the original one, i.e. its motion path speed is consistent across the whole length.
The *only* thing different about these two motion paths is their position on the sphere. Spacing, position and tangency are the same. It seems unreasonable that they should behave completely differently.

From Maya online help: "When you first assign an object to a motion path, by default, the object travels along the path at a constant speed."