I think they're pretty much the same. If someone says "She is a good singer" and you don't really agree with them, you could say "That's debatable." Most people would use "debatable" but "arguable" works too.

Generally, you debate (discuss) a topic, but argue (put forward) a single fact/statement. 1) "Whether or not I am the best singer is debatable" (Topic = 'whether or not I am the best singer') 2) "It is arguable that I am the best singer." (Proposed fact = 'I am the best singer') People do use 'arguable' in 1), but I think 'debatable' is nicer. you can't use 'debatable' in 2).