imho, cows are only good for beef. they can and will destroy a fence lickety split. they are big, dirty, and dangerous, as well as stupid.
goats are entertainment. they have wonderful milk (the dairy breeds do), wonderful meat, and are easy to move and handle. when dehorned, they don't tend to get stuck in the fence. i kept mine in field fence w/a single strand of hot wire about 12in or so above the ground, and they never got thru the fence-didn't even try, after they got bit as kids. they are clean (small pebbles for poop, not huge piles) and even a 5 or 6 yo can lead around a full grown doe that has been taught to lead. for that matter, a 5 or 6 yo that has been taught can milk a goat. it is true they are browsers and prefer to eat up, not down, but they can and will eat grass.
personally, i prefer a mix-dairy and meat goats and A (one (1)) steer for the beef, couple of hogs for the pork, and chickens to run around and break down the poop of all of them.
if it were one or the other- i'd vote goat every time. they are inexpensive to start with, the meat is very good and healthier than beef (more protein, less fat) and they are just plain safer to mess with. but, you do have to have good fences and animals that were raised in good fences and never learned to get out of poorly built fences.