Compared to a dot on a map that usually just narrows it down to an entire building?

If the sound is muffled and you can’t hear it, this sounds like it could narrow it down to a specific room or maybe even area of a room. Which is a huge improvement.

I haven’t personally used a Tile before, but my impression was “you get what building it’s in, then have to search everywhere til it’s in earshot”

The finding app has an arrow on it, pointing you towards the signal. So maybe the map has only building-level resolution, but once you're in the building you just follow the arrow until it says you're standing on it.

Tile trackers are accurate within +-90cm based on some empirical tests I did for using them to monitor my cat's activity throughout my house.

So Apple's +-30cm does seem to be a fairly major improvement, if true.

That’s a 60cm range, which is non trivial. It’s about the length of a human arm. Many desks are 120cm wide, so half of that.