With non manicured plants, you get a diversity of heights, widths, and general shapes. In addition to what was mentioned by Anne (or to further describe the hiding places and nests), a much greater diversity of insects, birds, rodents, and spiders will find their niche in a this more varied hedgerow. This will then correspondingly attract the creatures that prey upon them. In addition to this, the more plant species that are put in the hedge, the greater the potential for corresponding niches with associated creatures.
Let the trees and bushes grow up your fence lines instead of keeping them manicured. This way the wildlife has more cover to hide in plus more places for nesting areas.