According to Merriam-Webster, both these words *can* be used to refer to something the truth of which is in doubt:

[Debatable][1]:

>2a :  open to dispute :  questionable

[Arguable][2]:

>1 : open to argument, dispute, or question 

However, a second meaning for *arguable* is 

>that can be plausibly or convincingly argued

That is, *arguable* can be used to describe a proposition which someone wishes to present as true. *Debatable*, on the other hand (especially in light of the apparent synonymy of *questionable*), is often used to describe a proposition which someone wishes to present as false or at least unlikely; see for example Merriam-Webster's sample phrase

>the debatable wisdom of going back for another helping from the buffet

which, it seems, would indicate that *going back* is presented as unwise.

[1]:http://www.merriam-webster.com/dictionary/debatable
[2]:http://www.merriam-webster.com/dictionary/arguable