Bitcoin has a flat transaction rate for moving any amount of value. So yes, more expensive if the amount being transferred is low, and I mean really low.
Edit: tl;dr: problem with bitcoin's transaction fees is that they are not flat, but instead depend on non-obvious technical details of the protocol.
Also, pertaining to the original article, it's unclear if either ring signatures or bullet proofs can be made to work with an account model. Is there any examples of this?
*Bitcoin now measures transactions in weight, not size, a similar concept to Ethereum's gas (though much simpler)