Goats are:

• Easier to transport from field to field.
• Easier to erect temporary fencing to keep them in.
• Less likely to injure an idiot that hops the fence and harasses one.
• Easier to use on smaller plots.
• Less of a problem if one escapes.
• Cheaper individually to replace if someone steals, kills, or injures one.
• More tolerant of rough terrain.
• And yes, just like you said, will eat just about anything.

They're probably more difficult to sell for meat though.

They can quickly strip bushes and trees of all their bark that is in reach, killing them. Goats can be useful if not allowed to overgraze and then move on to the above. They have browsing preferences, like cows, and can be very, very stubborn about reaching their preferred meal at any cost. They are also skilled escape artists, unlike cows. They need to be managed carefully in a pasture, like any grazer.