I'm not an expert, but my understanding is that milling machines are generally used for metal, because they are more heavy duty, and routers are generally used for softer materials like wood or acrylic. I have access to both with my Techshop membership. The router is a lot easier to use and can handle much larger items, but we are not allowed to use metal on it.
Thanks for the tip about that angled bit! That will probably save me some bloody fingers.