One of the odd things about the new Apple TV is the fact that its available in a choice of storage sizes. Apple's own website seems to gloss over the fact; despite all the specs on the Apple TV page, storage sign isn't among them; its only when you get into the actual store page that the fact that there are two models becomes apparent.
If you plan to use your Apple TV primarily to stream movies, TV shows, and music or to play a few apps and games, you’ll probably be fine with 32GB of storage. If you plan to download and use lots of apps and games, choose the 64GB configuration.1 Keep in mind when making your decision, that some apps, when in use, do require additional storage.
The old (3rd gen) officially has no storage (in fact, it has 8Gb - but won't let you install apps.) So it would seem that 32Gb – four times as much as the 3rd gen – should be plenty, unless you're planning to load up with downloaded games.
That said, Apple does seem to have a history of under-loading the base model of its products; Macbooks with 4Gb of RAM long after 8Gb was considered a minimum for good performance (frustrating because RAM is relatively inexpensive – if you don't buy it from Apple), iPhones with 16Gb of storage – which is probaby enough if you don't use it as a camera, or want to regularly take your photos and videos off your phone, or want to keep music or video on there. The extra storage is relatively expensive (again) – but there are very few people who I can think of for who I would say it isn't worth the extra cost.
The Apple TV should be simple though. For someone using it as a TV/video device (most people, surely?), even Apple say that should be enough.
But this review of Facebook TV made me think that might not be the case. Think about this;
I click to another video in the horizontal feed, and it immediately begins playing in the big hero slot. Then, I click on the original video I was watching and it immediately begins playing right where I’d left off.
To make that work, you need a bunch of different videos cached on the device. And to make that work – you want to have a bunch of space to store that video.