Sure! The basic thesis, really, is that AP is very server-oriented, whereas AT is more oriented around the individual user and their data.
So, while your data obviously does live on a server in an AT world, you aren’t necessarily too fussed about which server that is, and it can move - account portability is listed as their main reason to not use AP. So AT’s focus is more around individuals in one giant federated network, whereas AP as it’s mostly used today is more about communities which are themselves interoperable. Out-of-the-box AT is less interested in building narrower, more gated communities, though they do say it should be able to be narrowed down to support that.
I’d say AT Proto appeals to folks like me who run essentially single-user Mastodon instances and just want to chat to - and discover - the whole network, and possibly also to folks who are on the really big instances where they don’t work so much as communities in themselves. It’s perhaps less useful for folks in the many Fedi communities that are quite self-contained and just happen to want to talk to the wider world.
There’s also a good point made about how moderation and server administration are decoupled.
I’d say do read the interview, it’s a good one and Nilay is as always a great interviewer. There’s also a brief FAQ on the AT Proto website: