Afaik, none. They both have models that play blu-ray disks and can read from an external HDD. They also have the basic streaming apps available and are faster than a smart TV so you could in theory use them as your only source of media and just use your TV as the output.

That being said, there are a couple things to be aware of:

• Not all blu-ray disks are created equal, so if you want 4k blu-ray you'll need a late model
• there are models that don't have disk drives; don't get them if you want to play disks
• if you want to stream you must connect to the internet. If you're connected the console WILL auto-update on you periodically. If you're just playing local content, don't connect, then this won't be an issue
• there's no traditional remote, instead you'll have to control them exclusively through the controller (🎮) and software menus

The only real differences you'll see are in how the ui is laid out.

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I'd take stock in the physical media you have. Are they blu-rays, DVDs, CDs, 4k blu-ray, uhd, etc? Then look at the consoles at your local pawn shop and check if they can play what you need. In general, newer models can play newer formats (like 4k), and XBox can play more total formats (newer PS dropped support for CDs).

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FWIW I have an XBox Series X almost exclusively for movies. My wife and I do play games on it occasionally, but we're both more PC gamers and I got the console with the primary intent to be a blu-ray player.