Actually, the local network security varies between regions and providers. Some regions has extended security features for private networks, but generally speaking, try to think of the private network as a region wide local area network without much internal security.
The key difference here is that while your public IP address can receive attacks from anywhere in the world, your private IP can "only" receive attacks from within the same region.
This issue affects any cloud that doesn't let you build your own private networks.
