Hi Charles
Yes you'll need hreflang tags on those two sites wherever you have duplicated content. I'm not sure about that sentence in bold that you found in another Moz post however referencing the Google guidelines on hreflang, they have the following:
- You keep the main content in a single language and translate only the template, such as the navigation and footer. Pages that feature user-generated content, like forums, typically do this.
- Your content has small regional variations with** similar content in a single language**. For example, you might have English-language content targeted to the US, GB, and Ireland.
- Your site content is fully translated. For example, you have both German and English versions of each page.
The second point is most relevant to you in this situation I believe. Duplicate English content targeting different regions.
I would NOT recommend using the canonical tag because that will seriously limit the visibility of the piece of content that is your non-canonical version. If you want exposure in Google UK for your .co.uk site and other versions of Google for your .com then use hreflang and Google will be able to understand how your content should be targeted.
Furthermore, if you want to target one specific country with your .com (e.g. USA) then you can use the country geotargeting report in Google Search Console.
All the best