The competition emerges as both can be used as a platform for ICOs and other kinds of crowdfunding, and also as a platform for "private currencies". Ethereum isn't really used much for its advanced smart contract functions. And Ardor's child chains have the advantage that no ARDR transaction fees would have to be paid for token transactions if a bundler is available.
As far as I know, this advantage is unique. Only in "empty blockchains" of Bitcoin-based coins, where zero-fee transactions are possible because of the low usage, this disadvantage does not exist, but empty blockchains aren't a sustainable model for a successful currency ...