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The advantages are mostly myths pushed by marketing, the RAW converter sucks, and the cameras are older/quirky. Not to mention Foveon goes to shit as you push the ISO. They do resolve a bit more than Bayer with the same pixel count (actual count, not 3x count), but if you need the detail you can go much higher with Bayer and have modern features, high ISO, universal RAW converter support, etc.
They do produce files out of camera that feel like slide film (higher contrast, saturated, moody), but you can get the same look on any camera with a little effort.