As far as I'm aware, you certainly un-publish your hub and put it elsewhere. You also need to be aware of the rules where you're planning to put it. Check the terms and conditions of the site it's going to, because some writing sites only allow content that has never been on the internet before (even though you may have deleted it from Hubpages).
You may want to start by writing about 10 completely new articles and putting them on another site - have 2 (or more!) sites going at once, until you see which one gives you better long-term traffic. I personally haven't moved my articles after putting them on Hubpages. But I don't see why you couldn't, so long as you unpublish on Hubpages first, AND check that the new site will accept articles that have been on the internet previously.