I have dairy goats (Old English) and Shetland sheep.
I have more to do with the goats - they need shelter, so come into a byre every night. They're around more, respond to me more, half-way between dogs and sheep I reckon.
So when it's time to do something with them, they're about and quite tame. They wear collars, I have a milking stand they can be persuaded to get up on and shut into. I don't have to worry about 'catching' them.
They make way more fuss than the sheep, about drenches, vaccinations, foot trimming.
The sheep need less attention, but when they do it's a morning's job to round them up, get them in, deal with them etc. They resist each step in the procedure.
The goats need double-height stock fencing, or wall-topping over drystone wall, if you want to keep them in. For all the Shetlands' escape-artist reputation, unless the walls have gaps, or the gates need lamb-bars underneath, they tend to stay where I've put them.