Let me start by saying I am not a dairy farmer, and we're discussing non-vegan things on a vegan space, so I want to respect this is their space and not get into too deep a discussion about this here.

I come to these spaces to try to learn to be more vegetarian/vegan. My personal feelings come from an ecology basis though, not a moral one like many here. I feel education is the way to promote these things, so I found some links with solid sounding data comparing water consumption between cows, goats, and sheep.

To stay on topic for this post, all are still worse ecologically than plant derived sources.. For your question though, sheep may beat out goats depending on what aspects you value most, but it's a very well researched and detailed field of study if you are interested. Big Ag means Big Data.

Anyway, here are your links, and to everyone else, I hope this is a respectful response, and if not, I will take the post down.

MILK SHOWDOWN: COW VS. SHEEP VS. GOAT

Dairy, Drought and the Drying of the American West

The Value of Water