I think one major difference with that is that animals can move around, go distances in search for food or mate, and thus make the animal densities per geography vary greatly. Birds migrate regularly, so their population densities tend to vary with seasons. Their mobility also depends on the availability of food, so animals go away if there are no food in the area.
Plants on the other hand don't move around faster (they can migrate by reproduction: it's their seeds moving around). Thus their densities tend to be more constant per season/life cycle.
