I've used both types of milk. Both work fine. Goat milk has more label appeal than cow's milk.
I grew up milking cows - I never want to milk anything again - if I can help it! Yes, I raise goats - Myotonic or Fainting goats but, I do NOT milk them. They are a heritage-bred meat goat. I buy my goat milk. My way of supporting another farmer.
Not to steal the show from this thread but, here's my latest Goat Milk Soap - an Igloo. I made this soap with plans to donate part of the sales from "The Business Day" of our Town's local Great Ice event. The proceeds were being donated to the local fire dept in honor of my friend & town mentor, who suddenly passed this fall. "Dwayne" was the catalyst behind our fire dept getting an air boat that could perform ice rescues on Lake Champlain. The boat now carries his name and has saved several lives. Our Great Ice event has been cancelled due to lack of ice but I plan to advertise the soap and will still donate to the cause.
Sorry for the long type............................