Make a copy of your company's job advertisement, and the competitor's job advertisement, and take them to management. There are basically two possibilities:
One, your company might have used some tool where you enter a few keywords, and the tool spits out a nicely written job advertisement. In that case, your competitor may have used the same tool, and being your competitor they have likely similar job requirements and may end up with a very very similar ad. Or both your HR and their HR might have used the same book "Effictive job adverts for dummies in 24 hours" :-) So if your company used a process where having identical ads by competitors is possible or likely, there may not be much you can do.
Two, they copied your advert. That would be copyright infringement, for commercial purposes, so if your HR person says "I spent 8 hours to craft this advert from scratch" your management might decide to sue them.