Actually, I'm fairly sure that neither game will be on cartridge. I said this when they were first announced back in or around September of last year, anything over 16GB has no chance of being on cartridge I'd say, unless they have an additional digital download but that defeats the purpose of a physical release. It's the prices of the games I take umbrage with. Selling a box with a digital code inside instead of a cartridge, I hate this kind of a release. Final Fantasy X / X-2 HD Remaster could fit on a 32GB cartridge but FF XII: The Zodiac Age is somewhere around 40GB on PS4. Given the lower specs of Switch, it should be smaller in size, perhaps if they made various languages as optional downloads, it too might be squeezed onto a 32GB cartridge. But it's irrelevant, as Square Enix will do no such thing.
Edit: It's strange, the product description of Amazon for both games say that they come with the game and manual. We need more clarity, surely they haven't got the complete games on cartridge, and if an additional digital download is required, then where's the usual white banner on top of the box art stating so?