What are some artificial ecosystems with more diversity than natural ecosystems?
In general, natural ecosystems have far greater biodiversity than artificial ecosystems. Human intervention has usually lowered biodiversity in an area as humans settle there--grasslands and forests are paved over, and animal species that rely on the removed producers decrease in number. Humans plant farm crops, eliminate "problem" species of plants and animals, and create single-species crops. In order for an artificial, human-created ecosystem to have greater diversity than a natural one, there must be some incentive for the humans to produce such a thing.
Zoos are one example of an artificial ecosystem with high animal diversity. Large-scale aquariums also have larger animal, and sometimes plant, diversity than surrounding areas. I have attached a link that discusses an artificial wetland that was created in order to deal with wastewater.
The simpler the ecosystem, the more fragile it is. If a homeowner has a large mono-culture of grass on their property, for example, a disease that targets that grass type will wipe out the entire lawn. If there are various types of native plants mixed in, the lawn is more likely to survive disease; not only will some plant types survive, but the plants that are susceptible will be further apart from each other and the disease less likely to spread.