I tend to think of "purposely" as meaning "on purpose", or intentionally, and descriptive of a singular incident; whereas "purposefully" more specifically describes a state of intent of doing something on purpose and/or proactively working toward a goal of some sort.

eg: "I purposely forgot to return a friend's call [because I didn't care to talk with her]" vs. "I purposefully avoided returning a friend's call", with the second instance indicating a more general goal.

Maybe a simpler way of stating this is that "purposely" means on purpose, whereas "purposefully" means with a purpose.

Does that make any sense?