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.