generally speaking ,there is no clear distinction between the two words .in some cases ,these two words can be used interchangeably .for example ,你用什么方法（办法）解决这个问题？i hope i can help you

I dont really think they have difference.

Genrally , is Thinking 办法and choose 方法。that is the different bewteen this two words . but in real life ,in some situations. they can exchange freely,no limition.

method and fonction

他们是有区别的。方法 is for something to do, 办法is for some problem to solve.