I don't know of a direct way to figure that out but testing keywords on google and seeing if your competition pops out in the paid links or even in the Organic results.
You could potentially use an SEO tool to check for keyword density of your competitors page. If they have done their job right they should target those specific keyword in their page.
Try this one: http://tools.seobook.com/general/keyword-density/
put your competitors web address and check which keywords come up the most, it should be what they are targeting.
The difficulty would be with long tail terms, which, by definition are not that common.