It's got company with the Barn Owl these days, and it thankfully doesn't seem to be going after native birds too badly.

As for Little Owl vs Morepork IRL:

From NZbirdsonline

A total of 219 little owls were imported and released by the Otago Acclimatisation Society between 1906 and 1910. Additional birds were released in the Canterbury region around the same time. They spread rapidly, and are common throughout the eastern South Island.

Little owls were introduced with the intention that they would limit populations of introduced finches and sparrows, and thereby reduce crop damage. There is no evidence that they have been effective in this, nor are little owls considered a significant threat as a predator to any native bird species. They are a major predator of the endangered Cromwell chafer beetle (Prodontria lewisi), and may limit the beetle’s population. The largely non-overlapping distributions of little owl and morepork are suggestive of competitive exclusion. This may be driven more by habitat preferences than direct interactions, but this has not been studied