The identity management is a big one. I’ve had my ActivityPub account get nuked when Nerdica offline, and my current ActivityPub server (Trom) is sometimes slow and misses remote events. Having an identity I control means that I don’t get my account nuked if something breaks, and I can participate within communities without being tied to their infrastrucure if the community is great while their infrastructure is not. It also works across different forms of servers - no needing accounts on Mastodon, Pixelfed, Writefreely, and Peertube in order to experience each form of social media on the network - on Nostr I can just use my same account across the network. It also makes me more tempted to host my own infrastructure, since if I get a case of the stupids, I can’t accidentally nuke my account.

I also like the protocol’s simplicity. It’s pretty lightweight, and pretty easy to extend with some custom code. While custom extentions would break normal stuff (adding custom stuff to shortform posts is just going to make your stuff not work with other people’s clients), creating something like a chess app or geocaching app is pretty easy. Even if said apps wouldn’t work with your standard shortform or longform clients, they’d still interact with other apps using the same custom code, and be useable with a standard account.

And, while I seem to be a minority in this thread, I also like the moderation structure of Nostr. There’s a few different ways to approach that:

• I use Nostr like RSS, I follow people I like and see their content - and I moderate it like I ‘moderate’ an RSS feed, i.e. choosing who I do and don’t want to see.
• There are other ways to moderate though, for example, by pulling people you follow from the whole network while only setting your global feed (if your client supports a global feed) to pull from specific relays.
• Or you could use something like Ditto, which is a Nostr relay behind a Mastodon front end. Ditto gives users a local feed and global feed (though I beleive both can be enabled or disabled), with the content on the Ditto server being capable of moderating content in the exact same way any Activity Pub server can (including accessing content or controlling moderation via the Mastodon API).
• Last, if I was famous or had people trying to spam me, I could also set my inbox relay (place where people send their replies on outbox model supported clients) to a relay I control, then set rules/filters on who’s allowed to reply and/or what content replies could contain.