Having lived in the city my whole life, I've got to say, we have chavs. Have you heard of GLC? they're literally one town away. Thats not to say there are more chavs than in anywhere else, because from my experience, it isn't the chavs that cause the trouble, it's just the trouble makers often also happen to be chavs...there's a very strong identity to the city, a stereotype really, that people here tend to be very upfront about things, which might lead to more late night stand offs in bars, but to be honest, I haven't really eyewitnessed that much crime in all the time I've been here.
I'd like to add that cardiff city centre, being quite a condensed area, has the most CCTV and police coverage of any city this side of Pyongyang. As someone above commented, town on a saturday night is bedlam, and the police are out in force to prevent violence, and this is pretty effective.
I'd imagine that newcomers learn of the hotspots soon (there aren't very many of them). I really don't think the crime rate/ chav prevalence is high enough to solely justify not coming here, it's a great little city ( That's an oxymoron and makes no sense, but it's really the best description for the place...)