Goats produce more milk for the amount of feed input.
They eat less overall, require less housing, less pasture, and will eat a wider array of plants than do cows. Therefore, you can have many, many more on the same amount of land and housing than one cow.
Goats have a higher butterfat content in their milk, and most good dairy does should produce a gallon per day, or more.
Does should produce at least twins or triplets every year, and if bred well, kids can sell for anywhere from 250.00 - 800.00 EACH.
Goats are smaller, easier to handle, and have loving, outgoing personalities.
Goat manure doesn't smell bad and is easy to clean up.
A 3-4 month old wether is a decent size and easily killed and butchered through by one person. They pack a LOT of meat on those frames, too. Also, you never have to spend one penny feeding them any grain to get them to a nice size - they do just fine pulled right from the teat/pasture/hay at this age and butchered.
Goats are easier to transport, show assist birthings, do medical treatments on, trim hooves etc...
If you want to produce beef as well, go to a local dairy who will often sell bull calves at birth for 25-75.00 apeice. You'll have to raise them on milk, which if you have 5+ milking dairy does should be easy to provide. They usually take a gallon or so of milk per day,which you can provide them if you have enough dairy does. So, you can get goat meat/milk, as well as get some beef, too.
I thought at one time I would like to have a dairy cow in the future. I now will never own a dairy cow, when goats are better producers, easier to care for, friendlier, cleaner - the list goes on.