Foto Showdown, I remember because my friend had it and only played it for a week since she didn't like how collecting monsters with the camera was annoying due to the color gimmick.
Digimon World Dawn and Dusk is closest enough in that it even has version and team exclusives, though any Digimon World game will scratch your itch.
World of Final Fantasy also fits that you get creatures and even call upon other FF characters to help you in battle, if you don't mind this...
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