best video app...prime video or apple tv?

Video quality and file size are related. iTunes Store content and Apple TV+ content are known for their slightly higher bitrate in order to achieve better quality.

But for phones, you can perhaps do with 480p or 720p instead of 1080p or higher resolution, thus also saving quite a bit on file size.

But mostly these apps are not very comparable, as they offer very different content (different shows).

Their visual quality is similar enough* to consider other features of their services.

• Amazon Prime Video needs purchases out-of-app on Apple devices, which is inconvenient.
• iTunes Store has a larger catalog.
• Some titles you may like will be on just one of these services, or maybe neither one.
• You may have already invested in one of these, so building a library in one place would be more convenient.
• You may like the UX/UI of either one more than the other.

* Both services take content from the source studio through an intermediate encoding house, to get content to their own specifications, which are not public, and could be different by title and date. The playback on the device will be decoded by the OS AV framework, not the app. So the app doesn’t make a difference for visual quality of movies.