I've been in both public, and private housing over the years. I can tell you this much, wherever you live you're going to face the same issues at some point. Public housing tends to get a bad rep because naturally people assume it's low life scum who live in them - which is completely wrong and stupid.
You may get a house with quite neighbours, you may get one with noisy neighbours. It doesn't matter what type of housing it is, thats a possibility anywhere you decide to live. Before accepting a property speak to neighbours, and not just the ones who are either side of you.