The closest feature to child chains that EOSIO is planned to integrate at the moment is side chains. However, side chains can be quite different depending on many factors, and it's difficult to reason about them before an implementation or something close exists.
I see that Ardor has a chart that is meant to compare side chains and their child chains, but the comparison is not directly applicable to EOSIO side chains.
For instance, they claim that "Side chains need their own network security and block processing." and although that's generally true, some EOSIO side chains may have the same block producers that will secure all networks at the same time (source). Similarly, the rest of their advantages can be simulated or already exist in EOSIO side chain proposals.
To read more about side chains in EOSIO, a more detailed explanation can be found in the InterBlockchain.io whitepaper, and an explanation of design decisions that support side chains in EOSIO can be found in the whitepaper.
Ardor has the child chain system where tokens holders can use the Ardor network without hold any of the parent coins.
Side chains can have their own native token which allows one to use the side chain, but to use the EOS mainnet, for instance, one would have to lock their side chain token in a smart contract that would allow them to use EOS tokens on the EOS mainnet.