Quote:
Hi, you can run spyglass twice, one with your site's url and once with the competitor's url, then extract data to a spreadsheet and compare it.

That's a good start, but you can finish off pasting the lists to LinkAssistantor SEO SpyGlass.
E.g. Linkassistant - start a project for your site and paste your list via File -> Import Plain Text. You can copy/paste URLs directly from SEO SpyGlass. Select all of them and add a tag or a not to them (e.g. "my backlinks").
Run File -> Import Plain Text once again and paste backlinks from your competitor's project in SEO SpyGlass. Exclude duplicates during that process (there'll be an option), and you will see new links in your project, the ones not having the "my backlinks" tag/comment.
Or, you could take the list of backlinks of your competitor, copy/paste them to a spreadsheet column and then click File -> New project Expert Options -> Enter Backlinks Manually and create a project for your site and competitors' backlinks. Update "Page info" for all the backlink URLs in this project. The ones that your competitor has and you don't will have a "No" in the "Links back" column.