My main concern is the publishing of videos to the Youtube site. It isn't hard to connect the video to the child's account on Kidzvuz and so someone coming across the video on Youtube can find that child's id at Kidzvus. There's information aggregation possibilities I'm not sure Kidzvuz are keeping an eye on. One video I watched of a kid playing a game revealed their game identity - from this kind of revelation, a viewer can put together a composite profile of a child from different platforms.
The Youtube question again - I tried out their claim that comments are moderated. They are not. My comments on the videos on youtube went through a split second after I hit post. Kidzvuz replied that it was a bug that they fixed after I identified this problem.
If I were a parent, I wouldn't rule out this site but I'd test and try out rather than trust their claims. Look at the other videos, see if there's stuff that should have been caught out, be mindful that kids inadvertently reveal stuff about themselves that can be put together with revelations on other sites and platforms.