According to Merriam-Webster, both these words can be used to refer to something the truth of which is in doubt:
2a : open to dispute : questionable
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.