tl;dr : For SEO, should I redirect from one to the other or list both on the DNS records?
It seems that most experts think that both www and non-www should exist. (Please correct me if I'm wrong.) And Google Webmasters Tools lets you choose which is the main one.
But: will a redirect give all SEO weight to one of them instead of splitting it? (There are other search engines after all, so setting the main one in Google Webmasters Tools might not be enough.) Will having both on the DNS records give them more importance? No difference?