Except you can check-in online with a Cat C if those particular class seats are available! Heck; I've just received an e-mail from emirates.com showing my son's itinerary for tomorrow and showing online check-in links - and he's got a Cat C ticket...
The other time a Cat C helps is that if the flight is payload restricted (as I had trying to get to Milan once on a 773) you have priority over freight. And that helps