There is no difference in pricing in Private or Public containers (databases). As seen on
https://developer.apple.com/icloud you get 40 requests per second, 2 GB data transfer, 100 MB database storage and 10 GB assets storage. And that's just for starter, if you happen to have more users the requests per second will scale upp and the storage will scale per user.
Although, if you exceed these limits, you'll need to pay $100 per extra 10 requests/s, $0.1/GB in data transfer, $3/GB in database storage and $0.03/GB in assets storage.