One difference is that Twitter no longer shows threads to logged-out users, while Mastodon does. If someone posted the same thread to both sites, the Mastodon one would be better to link to.
I think this is a misfeature that will hurt Twitter going forward. I don't bother clicking a link to a Twitter thread any more because I know I'm just going to get prompted to log into the account I don't have. And I don't care enough to use an alternate tool, so I just move on. I expect I'm not alone.