The word dubious is an adjective meaning hesitating or doubting. "Sarah looked dubious, but followed her boss's orders." It can also describe something suspect, or not to be relied upon. The word is sometimes used to mean something morally suspect or of questionable value. "Pyramid schemes have come into disrepute because of dubious sales methods."
Doubtful is an adjective that means feeling uncertain about something. "Doubtful of the bridge's sturdiness, Tom took another route." It can also describe something not known with certainty. Something improbable or not established as genuine may be called doubtful. "The new drug was of doubtful effectiveness."
Dubious and doubtful share an etymological root in the Latin dubium, which means "a doubt" and "dubius," meaning "doubtful." Other terms with similar meanings include ambiguous, enigmatic, equivocal, problematic and questionable.
The New Oxford American Dictionary puts the terms in this context: "If you are doubtful about the outcome of a situation, you might be understandably dubious about getting involved in it." Both words express suspicion, indecision or lack of clarity, but doubtful carries a strong connotation of uncertainty, to the extent that the thing described is presumed to be worthless, invalid, unlikely or doomed to fail. Dubious is not as strong, suggesting hesitation or misgivings. If you are doubtful about the outcome of a situation, you are fairly certain it will not turn out well. If you are dubious, you are wavering in your opinion.