Is using a local DNS cache server imore secure than using a DNS server from a router?
Confidentiality standpoint: Not much really, it does combine your requests with others behind the device, and won't be making them as often as if you were doing it uncached.
Availability standpoint: if a site stops responding to DNS requests sometimes the DNS cache can maintain those requests for a long time (depending on the cache ttl.) Conversely, if a site is using DNS to perform load balancing or failover, you might be impacted if the site goes down and they switch to another IP for the host behind the name.
Integrity standpoint: Cache poisoning is a risk, you might be succeptable to it currently (or in the future.) It could also be used by an attacker, if the device was compromised, to redirect DNS requests to a hostile service.
None of these reasons are huge negatives, you can have all of these things applied at almost every layer of your network. Even Firefox has a DNS cache believe it or not. If you have the need, I'd use one. Just follow good security discipline while managing it.