It helps manage a social media presence for anyone who relies on it, I.e. artists and general celebrities. George Takei, for example, already posts the same things to mastodon and bluesky (no clue about nostr) and has a very large following on both platforms because of it.
I don’t, and I won’t make that possible for myself either. I don’t need to spend even more time on the internet interacting with bots, AI, ads and spyware.
While ActivityPub is a way for social media instances/server to ask for a user feed or do updates (likes, comments, etc.), Nostr is a media format and more client-side protocol.
ActivityPub. Servers talk to each other, users are talking with servers in different language, like Mastodon talking Mastodon API. Users log in to their servers and have an ID there.
Nostr. Users have ID for themselfs, servers only act as a proxies to deliver a message, feeds are stored on devices, account do not live on any single place. Both users need to have at least one server common for each other to see their feed.
Honestly I think while ActivityPub is a nice glue, Nostr is already obsolete.
In my opinion problems that Nostr is trying to solve should not be dealed with making an Peer2Peer social media app, but rather with universal P2P network.
Decentralized networks like Yggdrasil or I2P do anything Nostr can do and are not limited to only posts, but can deliver any data just like the Internet. I host my own Minecraft server on Yggdrasil for example.
Relay/instance admins can choose which content goes through their relay on either platform
On nostr, your DMs are encrypted. In Mastodon, the admin of the sender and receiver can read them, as can anybody else who breaks into their server
On nostr, a relay admin can control what goes through their relay, but they can't stop you from following/DMing/being followed by whoever you want since you are typically connected to multiple relays at once. As long as one relay allows it, signal flows. Nostr provides the best of both worlds: moderated "public squares" according to your moderation preferences, autonomy to follow/dm/be followed by anybody you want (assuming that individual user hasn't blocked you).
On mastodon, your identity is tied to your instance. If your instance goes down, you lose your follow/followee list, DMs, etc. On Nostr, it's not, so this doesn't happen. Mastodon provides some functionality to migrate identity between instances but it's clunky and generally requires to have some form of advanced notice.
Both have all the same functions as twitter: tweet, reply, re-tweet, DM, like, etc.
Problem with Nostr:
Relays are useless because we already have proper universal networks that on application level allow us to just send messages straight from device to device.
It would be much better to invent message format and just use Yggdrasil, I2P or GNUNet to send it.
While Nostr invent a format and then invent very dumb way to send it - connecting all users to as many static nodes as possible.