Basically, they taste very similar. Fresh goat milk is slightly sweeter than cows milk, best exhibited by our grandkids who call it "juicy milk". When I asked them why they called it that, they said it tastes sweet like "juicy juice". Leave it to kids. I've heard many people say they don't like goat milk, only to find that they had only tasted canned goat milk, and had never tasted fresh goat milk.
My step daughter lived with us for a year. She was a city girl and was not happy about living on a farm, but she was going thru a divorce and had lost her job, and had no choice. She wanted nothing to do with our goats, and announced that goat milk is nasty. Little did she know, that since we had a dairy goat farm, the pitcher of milk that was always in the refrigerator was raw goat milk. She is a heavy milk and coffee drinker and we never told her that she was actually drinking goat milk, though she never seemed to wonder why our milk was always in a pitcher and not a milk container. One day she had some friends over at our house and one of them asked what goat milk tastes like. My step daughter instantly said it was nasty. My step daughter's friend was drinking a glass of our goat milk, and I asked her how the milk she was drinking tasted. She said, "Actually, this is the best milk I ever had!" I quietly told her, "Then I guess you like goat milk." My step daughter almost fainted.
Goat milk is actually healthier than cow milk. It has smaller fat globules that are more easily digested. It is naturally homogenized. And people who are lactose intolerant can often tolerate goat milk. It is also the universal milk for orphaned baby animals. Almost any baby animal can be successfully raised with goat milk.