Apples and oranges.

Wireguard is a VPN technology. DuckDNS is a service that lets you create a subdomain on the duckdns TLD and point it at your server. They do completely different things.

You would use DuckDNS if you don't want to rent your own domain ("rent" because it's a recurring payment for something over which you have only nominal control). It provides no security, no access control, and it creates no network. It's just a pointer in the global DNS DB.

Wireguard is a VPN technology, for creating private networks.

One is like a mailing address. The other is like a strongbox. You could give the strongbox to a friend to deliver it to someone who has the key (Wireguard). Or you could write a message on a postcard and mail it (DuckDNS). Or you could put the address on the strongbox and mail it (DuckDNS + Wireguard). The point is, they serve completely different functions.

The two could be used together.