The natural phrases are: You are your only competition. Your only competition is you yourself. Your suggestions sound a little awkward but would be understood.

They're both grammatically correct. The second one sounds more matter-of-fact and the first one sounds more marketingy.

“Yourself” sounds more taught

Both are valid. The first is blunt & snappy. The second is a smoother, more educated way of speaking.

Both words are needed when you use "yourself": "Your only competition is you yourself." The pronouns "yourself", "itself", "himself" emphasize something, and that thing needs to be stated. Since "you" is the thing being emphasized, you need both words. Here's another example: "the mountain climber climbed Mt. Everest itself" adds emphasis to "Mt. Everest".