They share the same parasites and on the whole, the goats are more affected by them than the sheep.
I keep my goats and sheep separate - well, I try. When the goat kids escape the sheep are quite interested in them but the goats don't like the sheep - maybe they would if they had started out together.
I have two paddocks, which I rotate, which are goats only and then separate fields, which I rotate, which are sheep only. So they're only the other side of stock fencing from each other sometimes but I feel that I'm keeping the goat land clean of worms from the sheep.