दुर्गन्ध is more formal while बदबू is most commonly used in everyday conversation. Both words mean a foul odour.
Why we don't likeee this fragrance, But what is the fragrance?-(Funny part)
What's the word for 'smell' (especially for bad smell) and odour?
Good smell: खुशबू/सुगंध
Bad smell: बदबू/दुर्गंध