There is nothing to tie the two sites and their content together. Nothing will update the two as they are completely separate.
If you would like to use a feed in the sidebar widgets of one of the sites, you can do so, highlighting the duplicate content from one site on another. If you make changes to the content, the feed might be updated, though not always, on the other site.
There is no way to create a cross-site update.
Be aware that the exact same content on duplicate sites could result in penalties and copyright issues with search engines (SEO) unless it is clearly stated why the content is being duplicated, unless you are just moving from one site to another and closing down the other site. If so, then choose to export and import the content to the new site and close the old site down.