I wouldn't really frame it in terms of "competition", but rather the issues the shows addressed. Daily Show and Maher were indeed closer in format to Tough Crowd, but they were a lot more politically correct in tone and subject matter. Many of their favorite targets were safe ones: Republicans, white trash, Christian fundamentalists, etc. You wouldn't see them openly poke fun at blacks or gays or anything other that's controversial, which is the kind of stuff South Park, Chapelle Show and Tough Crowd would do, which is why I'd place them firmly in the "edgy" category.
And while South Park and Chapelle Show had the defence that they were sketch shows, Tough Crowd featured real people ostensibly telling their real opinions in heated arguments with eachother. It doesn't surprise me that it made the suits a bit nervous, especially if the ratings weren't spectacular enough for the bean counter logic that determines what politically incorrect content was worth the effort to air. Two seasons and they ended it.