Mastodon is probably the closest to a "popular" alternative that isn't too different from Twitter. It has some genuinely good options compared to Twitter (you can decide private/public on a post-by-post basis, and it has a good content warning/tagging system), but also some cons (there are some different security worries due to how it's set up, and it can be confusing figuring out where you want to make your account). But by far its biggest problem is that as long as people aren't mass-migrating to it, none of your friends are on it.
Technically Tumblr is another option, but it's closer to regular blogging than microblogging. It's... sorta decent for sharing content (and fantastic for shitposting) but it's not the best option for socializing imo. There's also Dreamwidth, I guess, but that's more for long-form blogging à la Livejournal, even if there's a comment system.