The big difference is that the original intended text is encoded in the URL. An element-id fragment is better than just a URL but will often be less granular than the exact text being linked (e.g. a heading).
If you're looking to link a citation to a statement, having the text is far more useful since the person following the link doesn't have to now find the statement in a potentially large and broad section. Also, if the page has since changed and the text no longer substantiates the cited claim, that'll be immediately apparent.
The extension uses a new URL fragment addition that Chrome has shipped: https://github.com/WICG/scroll-to-text-fragment so these links will work on any Chrome/Chromium-based browser. (in non-Chromium browsers without the extension the link will load but the fragment wont be recognized)
The hope is that this is useful and adopted by other browser engines and links like this would eventually be interoperable.
If you're looking to link a citation to a statement, having the text is far more useful since the person following the link doesn't have to now find the statement in a potentially large and broad section. Also, if the page has since changed and the text no longer substantiates the cited claim, that'll be immediately apparent.