In practice, they both mean "smelly".
"odorous" = has a bad smell, a bad smell is a quality of the thing
"odoriferous" = produces a bad smell, the smell originates from the thing
You may want to distinguish:
a) a thing which has become "odorous" because of an external factor (e.g. My son's nappies become odorous after some time) from
b) a thing which by its very nature is "odoriferous" and so produces a bad smell, such as certain types of plants and herbs
Both words are very formal and unheard of in everyday conversation. Odoriferous is academic.