Additional app storage and the ability to store/download media in apps that support it.

From my (admittedly now hazy) understanding, everything in Apple TV land is supposed to be purgeable. So nothing should stop working on a 32 GB Apple TV unless it for whatever reason needs 64 GB of data on disk. This will of course mean that the 64 GB model is faster in caching scenarios, but it’s IMO an unnecessarily complex decision for an already expensive product in the space ($179 for 32GB!)

It's for games, apple tv supports a lot of games that are modified for the large form factor and can get quite large(like crossy road)

How many apps will I have to install to run out of space on my 32GB Apple TV? Curious how many people this has actually happened to...

Now, with Apple Arcade, it is very easy to run out of space. It made no sense at the beginning, though.

Maybe it's there in case you run out of swap for Electron apps.

I’m fairly certain that it will hold more of screensavers (at 950MB each), and they are honestly my favorite part of the device. If you don’t have broadband the idea of a bigger cache of content seems worth a nominal fee.

With Apple Arcade and recently added support for Xbox and PS4 controllers, space may become a constraint.

When the Apple TV first launched, you were limited to 200MB of an initial download and 20GB total counting later-downloaded on-demand resources. These on-demand resources in theory automatically get flushed out, so the HD space serves more like a cache. So the 32/64GB has a very tenuous relationship with performance before, and now that it's been raised to 4GB install probably will not be nearly enough space. It's a weird device.

Apps, e.g. games?

Apps and Games, genius.

Oh, because people are regularly installing the 7.8GB Xcode update?

Aside from the fact that I doubt anyone downloads that many apps, from my understanding Apple TV makes you use on-demand resources for anything above 4GB. That means that old resources automatically get flushed out, so the actual benefit of those extra 32GB is more of caching-feeling behavior.

I use Infuse with my NAS and it uses GBs of local storage for caching previews and thumbnails.

There are quite a few storage hungry apps least of all the screen savers.