I'm not sure how this relates to the parent comment, but there
are free encrypted DNS services out there, though the same can't be said for encrypted and anonymous ones (which is, frankly, a hard problem to solve, realistically speaking).
With encrypted DNS you're just shifting the burden of data privacy away from the local network to the DNS operator. How you determine which operators to trust will probably vary from person to person.
Anyway, the major difference here would be that a VPN will encrypt all traffic in a tunnel, from your DNS requests to your actual followup web requests. On the flipside, you may use encrypted DNS to look up records for a domain that serves content over an unencrypted connection.
