My reply may not be too useful because most of Australia's not known for having problematically lush grass...
Anyhow, my two cent's worth:
Goats are classified in the feeding category of browsers, not grazers like most cows and horses. Some sheep breeds are grazers, others browsers, which may be why your sheep didn't keep on top of the grass. As far as I know, dorpers and boers are two of the goat and sheep breeds most reliably grazed, both being heavy-production meat breeds so more likely to eat the richest source of feed possible. Older, heritage breeds are more likely to be browsers whose main interest/diet staple is naturally leaves, buds, bark, twigs, roots, weeds, herbs, etc rather than plain grass, especially the popular modern agricultural breeds and strains of grass.
Knowing what breeds of goat and sheep you have, as well as what environment their recent ancestors were raised in, would answer your questions pretty reliably.