My sitemap generator has created a sitemap.xml and sitemap.xml.gz file. Should I include just the .gz file in the robots.txt or both?
And does it do any harm to submit both sitemaps to Google et al?
As Closetnoc mentioned in his comment, GZ is just a compressed version of your text sitemap. So my answer to your question
Should I include just the .gz file in the robots.txt or both?
There is no point in submitting both sitemap.xml as well as sitemap.xml.gz. Most of the search engine bots can read the compressed content. So if you are submitting sitemap.xml it's enough or sitemap.xml.gz is enough.
does it do any harm to submit both sitemaps to Google
I don't find any valuable source to say that Google will harm you in this case also from this page you can see that you will not be penalized by Google.
Google - Webmaster Support on Sitemaps: "Google doesn't guarantee that we'll crawl or index all of your URLs. However, we use the data in your Sitemap to learn about your site's structure, which will allow us to improve our crawler schedule and do a better job crawling your site in the future. In most cases, webmasters will benefit from Sitemap submission, and in no case will you be penalized for it."