You can tell from Ben's excellent response that suffocate is more severe than stifle. To suffocate would mean to kill, but stifling merely inhibits.

Interesting question. The two share the same meaning when used in the sense of making it difficult for people to breathe. When used to mean "restrain, constrain, prevent or suppress an activity or an idea", "stifle" cannot be replaced by "suffocate". Thus, "to stifle a yawn", "a taxation system that stifles entrepreneurship", "his emotions were stifled by stern parents", "her growth was stifled by malnutrition". When "suffocate" is used in the sense of "oppress" or inducing a sense of being trapped, it can be replaced by "stifle". Example: As an artist he felt suffocated in the Soviet Union.