Amethyst is a vivid purplish-pink, and from my understanding, magenta is more of a rose. (I'm madly in love the amethyst; it's super-saturated and gorgeous!)
Magenta is more pink and Amethyst is more of a purple-pink. Amethyst is such a rich, saturated color, it's adorable!! Between those two colors, NO contest!! the winner is Amethyst!