What is the Difference Between 方法 and 办法? Both have comparable definitions of "method", "manner", "means", etc. and describe or define a way of doing something.  The phrase 没(有)办法 is often used to deflect responsibility by claiming powerlessness.  Aside from being more common in colloquial speech, does this make 办法 more general?  Anecdotally, 方法 is encountered frequently in instructions.  Does this make 方法 more technical?
I don't think you guys are completely understanding it, there is a philosophical difference in the two words. It's possible to 有方法但是没办法. 方法 refers to the general method or way something can be done. 方 means prescribed, 法 here can be understood as way. 

So 方法 is the general or prescribed way something is done that humanity has discovered. 办 means doing，法 here also means way. 办法 refers to someone specific actually doing it. For example:

我的病其实治疗方法很简单，就是每天跑步。但是没办法，因为城市太拥挤所以没有地方跑。Here, I know the way to cure my illness, but I can't specifically carry it out due to individual circumstances.