Google's webmaster tools does show the relevancy of particular keywords associated with a particular site, you might want to try it out. There are others as well but I'm not particularly sure which are best.
If you know how to do a keyword research and moreover if you know how to research your competitor there is no need for a tool to figure it out what keywords your competitor is ranking for.... Also On-Page SEO Factors can give you a good idea too for the keywords they are trying to target.
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I get this info for free from Alexa.com -- put in any URL and they'll tell you a 'world' of keyword density % and other info for the keywords they're most using.
That is your answer. Nothing left to say! Other than what SEMRush doesn't find, you can check for manually. Typically, SEMRush will find more than you can right off the bat.