CoStar Group Inc., one of the world’s largest commercial real-estate data companies, has taken direct aim at longtime competitor Xceligent with a lawsuit alleging Xceligent has been involved in “brazen and widespread theft” of its data and photos, according to legal papers filed Monday night.

In a lawsuit filed in federal court in Kansas City, Mo., CoStar alleged it has found thousands of examples of its copyrighted photos and data on publicly accessible portions of Xceligent’s site. It also alleges that Xceligent contractors...