This is his worst idea yet.This is his worst idea so far. Are they same? Which sounds natural?

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Yes, they're pretty much the same. Both imply that he might have even worse ideas to come, but that this one sets the record to date, up until now. Google Ngram Viewer (based on published books, not the web) indicates that "worst yet" is about four or five times as common as "worst so far." (The exact string with "idea" in the middle, or "suggestion," or some other noun, doesn't appear.) Both phrases appear in the corpus of contemporary American English (CoCA), in a soap opera corpus, and in a web-based corpus, although "yet" seems in the latter more common. Also, returning to the CoCA, "worst yet" (without "idea") also appears five times more frequently than "worst so far," and "worst _nn* yet" appears 30 times, vs. "worst _nn* so far" appearing 7 times, where "_nn*" means "any noun" (idea, moment, day, part, year, pain, flooding, etc.). I personally also would be more inclined to use "yet," but "so far" isn't unnatural.