Read the rest of the thread.
I'm a supply teacher and have worked in a huge range of schools in so many different areas with children from ask walks of life and, from what I've seen, yes: MC parents talk and listen to their children more, which is obviously a good thing, and are happier to let their children express themselves more. Also, as pp said, they are happier to take up more physical space and push themselves and their dc forward. WC parents seem to have a much lower tolerance for their children's behaviour, especially when they're messing about and getting in their or other people's way and I think this is possibly because of the fear of being judged more harshly.
WC parents seem to have less time and energy for the dc, in part I think because they're already coping with working long hours in physically demanding jobs, less money, less space and, potentially, more social or financial problems. They tend to shout more and just expect their dc to fall in line, perhaps because that's how they were parented and maybe because they don't have the language skills needed to talk about and explain their reasoning.
MC parents sound more feeble and wordy when telling their dc to behave. Where a WC person might simply yell, "Will you lot pack it in?!" an MC parent would get down to their level and talk at their dc, explaining what they did, why it was wrong and what they should do instead.
Personally, I think the best way is a mix of the two. That is how I try to manage my own dc as well as the children I work with.
I live a more middle class world now, through dh and his family, as well as through the work that I do and the hobbies we have, but I was born and brought up in a stereotypically WC area with parents who all (incl. my stepdad as well as my actual dad) had blue collar jobs and worked 6 days a week yet still could barely afford to keep the roof over our heads. We still live in social housing though but it isn't as rough as it used to be.