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301 the domain over to capitalize fully but it sounds like you might want to keep both sites active. If you have content that you want to move over or is ranking, be sure to create separate 301 from the old url to the new url. The page that receives the 301 will benefit from that. In many cases, the new url will rank in the place of the old one. If they have pages that have great backlinks (like an about page or products page) but you don't really want to move them over and want to just delete them, then just 301 those urls to relevant urls on your site and you will benefit from their links. Hope that helps! Good luck!